Cognitive radio spectrum sensing with improved edge detection of frequency bands

ABSTRACT

A spectrum sensing method for cognitive radio wherein spectrum holes are detected in a wireless environment having spectrum scarcity. First, a cognitive radio user (CR) determines the power spectral density (PSD) of a wideband signal and detects subbands within the wideband using wavelet transforms (WT). WT coefficients are calculated by convolving the PSD with first derivatives of wavelet smoothing functions. The extrema of the WT coefficients demark frequency subband edges. Detecting subband edges becomes more robust against noise by median filtering the PSD before calculating WT coefficients, summing over WT coefficients with different scale factors, and suppressing WT coefficients below a noise threshold. After identifying subbands, the CR determines subband availability by measuring the subband power and signaling the power to a fusion center receiving power measurements from multiple cooperating CRs, and final decisions are based on data and decision fusion.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application titled Cooperative Cognitive Radio Spectrum SensingUsing a Hybrid Data-Decision Method, attorney docket no. 419762US, isincorporated herein by reference.

BACKGROUND

1. Field of the Disclosure

The present invention relates generally to cognitive radios, and moreparticularly to spectrum-sensing cognitive radios.

2. Description of the Related Art

It has been proposed in Z. Tian and G. B. Giannakis, “A Wavelet Approachto Wideband Spectrum Sensing for Cognitive Radios,” in 2006 1stInternational Conference on Cognitive Radio Oriented Wireless Networksand Communications, 2006, pp. 1-5, herein incorporated by reference inits entirety, that spectrum sensing for cognitive radio wirelesscommunications can be improved by using wavelet transforms to detectdiscontinuities in a power spectral density (PSD). When considering awide band of interest without prior knowledge of how the wide band hasbeen sub-divided into frequency bands for allocated primary users, thefirst task of a cognitive radio user is to discover the boundaries andextent of each subband. Only then can the cognitive radio user begin toanswer the question whether the individual subbands our being used bythe primary users or if the subbands are available to an opportunisticcognitive radio user. Using dormant subbands allocated to primary usersprovides an efficient solution to the challenge of bandwidth scarcity.

Modernly, spectrum for wireless communication is becoming scarce asdemand continues increasing. Cognitive radio is seen as an excellentsolution to the problem of spectrum scarcity by efficient utilization ofthe radio spectrum. Cognitive radio achieves this by making wirelessnodes aware of their environment. The wireless nodes then modifyparameters in real-time, based on predicted availability of allocatedfrequency bands. The most important operations of a cognitive radio isfirst sensing the targeted spectrum, and then deciding on theavailability of spectrum in order that secondary users can benefit fromunused spectrum. Spectrum sensing for cognitive radio is a verychallenging task. It requires both accuracy and efficiency in order fora cognitive radio system to work effectively.

Traditional wireless systems operate under the policy of static spectrumallocation. Once a wireless service provider gets a license for using acertain band from the commercially available spectrum for a particulargeographic location, he and only himself has the right to operate inthat frequency band no matter whether he wants to use it 100% of thetime or only 10% of the time. Any unlicensed user is prohibited tobenefit from the licensed frequency band. As the trend of wirelessservices is shifting from voice-only to multimedia services, e.g.,mobile TV, the service providers are demanding higher and higherbandwidths. Realizing the fact that the spectrum band is a limitedresource, society is at the verge of spectrum unavailability for newwireless systems. In addition to this problem, a more disappointing notepublished in a FCC survey report pointed out that the spectrumutilization in the 0-6 GHz band varies from 15% to 85%, meaning that theactual licensed spectrum is mostly underutilized in vast temporal andgeographical dimensions, as discussed in FCC, “Spectrum Policy TaskForce Report,” ET Docket, 2002, herein incorporated by reference in itsentirety. Hence, this inefficient utilization of licensed spectrum canbe thought of as the outcome of wasteful static spectrum allocation. Inorder to solve the problems of spectrum scarcity and inefficientutilization, both researchers and policy makers got attracted to therecently introduced concept of cognitive radio, which was originallydiscussed in J. Mitola and G. Q. Maguire, “Cognitive radio: makingsoftware radios more personal,” IEEE Personal Communications, vol. 6,no. 4, pp. 13-18, 1999, herein incorporated by reference in itsentirety. Recently, the IEEE 802.22 cognitive radio wireless regionalarea network (WRAN) standard was introduced as the first effort towardsthe practical use of cognitive radio, as discussed in C. Stevenson, G.Chouinard, S. Shellhammer, and W. Caldwell, “IEEE 802.22: The firstcognitive radio wireless regional area network standard,” IEEECommunications Magazine, vol. 47, no. 1, pp. 130-138, January 2009,herein incorporated by reference in its entirety.

Cognitive radio is an intelligent wireless communication system that isaware of its surrounding environment (i.e., outside world), and uses themethodology of understanding-by-building to learn from the environmentand adapt its internal states to statistical variations in the incomingRF stimuli by making corresponding changes in certain operatingparameters (e.g., transmit-power, carrier-frequency, and modulationstrategy) in real-time, with two primary objectives in mind: 1) highlyreliable communications whenever and wherever needed; 2) efficientutilization of the radio spectrum. In effect, the whole operation of acognitive radio can be represented graphically as a cycle, the so calledcognitive cycle, as show in FIG. 17.

The concept of a cognitive radio (CR) network has been efficientlyexplained in S. Haykin, “Cognitive radio: brain-empowered wirelesscommunications,” IEEE Journal on Selected Areas in Communications, vol.23, no. 2, pp. 201-220, February 2005, incorporated herein by referencein its entirety, and in I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S.Mohanty, “NeXt generation/dynamic spectrum access/cognitive radiowireless networks: A survey,” Computer Networks, vol. 50, no. 13, pp.2127-2159, September 2006, incorporated herein by reference in itsentirety. This intelligent radio has the cognitive capability to senseits surrounding environment, and to determine appropriate operatingparameters for it in order to adapt to the dynamic radio environment,all in real-time. The fundamental role of a CR is to acquire the bestavailable spectrum for its users, based on its cognitive capability andre-configurability. Since most of the commercially available spectrum isalready allocated, the real challenge is to share seamlessly the unusedspectrum of the PU. Consider an example model of spectrum usage acrosstime and frequency displayed in FIG. 1.

The interference-based detection method calculates the maximum amount ofinterference that the primary receiver could tolerate. As long as thecumulative RF energy from multiple sources, including the secondaryusers, is below under a certain limit, the secondary users are allowedto transmit in a specific spectrum band. One model to measure theinterference at the receiver was introduced by FCC in FCC, “ET Docket No03-237 Notice of inquiry and notice of proposed Rulemaking,” 2003,herein incorporated in its entirety by reference, referred to as theinterference temperature model. Using this model, a radio receiver canbe designed to operate over a range at which the received interferencelevel is below the interference temperature limit. The limitations ofthis model are that it needs information about the unlicensed user'ssignal modulation, activity patterns of the primary and secondary users,in addition to having control over the power levels of the SU asdiscussed in T. X. Brown, “An analysis of unlicensed device operation inlicensed broadcast service bands,” in First IEEE International Symposiumon New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005,pp. 11-29, herein incorporated in its entirety by reference. Also thecognitive user may not be aware of the exact location of the primaryreceivers, which makes it impossible to measure the influence of thecognitive user's transmission on all the potential primary receivers.Because of the inherent complexities in the receiver's interferencedetection method, the method has gained less attention as compared tothe transmitter detection methods for cognitive radios.

Transmitter detection techniques have attracted most attention becauseof their simplicity. When this technique is used, the cognitive radiofocuses on the local observation of the signal from a primary user(transmitter). Transmitter detection can be performed either with onecognitive radio or by a group of cognitive radios cooperatively sensinga targeted spectrum band. The latter case is sometimes referred to ascollaborative (cooperative) detection as discussed in A. Ghasemi and E.S. Sousa, “Collaborative spectrum sensing for opportunistic access infading environments,” in First IEEE International Symposium on NewFrontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005, pp.131-136, herein incorporated in its entirety by reference. These(transmitter detection) techniques can be further divided intoBlind/Semi-Blind Spectrum Sensing and Non-Blind Spectrum Sensing asdiscussed in R. Umar and A. U. H. Sheikh, “A comparative study ofspectrum awareness techniques for cognitive radio oriented wirelessnetworks,” Physical Communication, August 2012, herein incorporated inits entirety by reference. The key difference among these schemes liesin the amount of a priori knowledge about the Primary User (PU) signalthat is required by the cognitive radio to perform spectrum sensing. Theformer approach (Blind/Semi-Blind SS) is usually used when the CR haveno prior information about the characteristics of the primary usersignal, channel, and the noise power. The best possible knowledge the CRcan have is the estimate of noise variance, hence the term Semi-BlindSS. Energy detection as discussed in A. Sahai and N. Hoven, “Somefundamental limits on cognitive radio,” Allerton Conference on Comm.,Control and Computing, 2004, herein incorporated in its entirety byreference, and discussed in H. Urkowitz, “Energy detection of unknowndeterministic signals,” Proceedings of the IEEE, vol. 55, no. 4, pp.523-531, 1967, herein incorporated in its entirety by reference, andstatistical-analysis-based detection falls under the category ofBlind/Semi-Blind SS. When prior information is not available or cannotbe extracted by the CR, Energy Detector is the best and simplest optionto perform sensing. Energy detection is the least demanding approach asit makes the receiver implementation task relatively simple. Under thecategory of Non-Blind Spectrum Sensing, we have the followingtechniques: 1) Matched Filter detection, and 2) Cyclostationary featuredetection, as discussed in A. Ghasemi and E. S. Sousa, “Spectrum sensingin cognitive radio networks: requirements, challenges and designtrade-offs,” IEEE Communications Magazine, vol. 46, no. 4, pp. 32-39,April 2008, herein incorporated in its entirety by reference. Matchedfilter detection and cyclostationary feature detection techniquesrequire a priori knowledge about the PU signal.

A cyclostationary feature detector is robust to noise power uncertainty.The cyclostationary feature detector can also differentiate between a PUsignal and other CR users' signal provided that all the signals exhibitdifferent cyclic features, which is usually the case. However, thecomplexity of the cyclic feature detector comes from the facts that itrequires the knowledge of different signal's modulation formats, as wellas requires long observation times. These complexities make the featuredetector implementation less favorable as compared to energy detector.

Wavelet based sensing falls under the category of Energy Detection. Therelationship among all of these approaches is summarized by the branchdiagram shown in FIG. 18. Wavelets are simply a set of basis functions.A wavelet is effectively a limited-duration waveform that has an averagevalue of zero. The wavelet transform (WT) is a mathematical tool usedfor projecting signals, similar to other tools that are used for signalanalysis, e.g., fourier transform (FT). A comparison of Fouriertransform and wavelet transform basis functions is shown in FIG. 19.Fourier analysis is perhaps the most well-known transformation to date,which transforms a time-domain signal into the frequency-amplituderepresentation of the signal. The FT provides the global information onfrequencies presented in the signal regardless of the exact time theyappear in the signal. When looking at a Fourier transform of a signal,it is impossible to tell when a particular event has happened. Thisproperty, on one hand, does not negatively affect the suitability of FTto stationary signals, but, on the other hand, makes the FT unsuitablewhen the signal being analyzed is non-stationary. For analyzingnon-stationary signals, a transformation technique that can providetime-frequency information is necessary. Instead of the traditional FTtransformation, we focus here on the WT. While the FT providesinformation only about the frequency components contained in a signal,the WT provides both time and frequency or time and scale representationof a signal under analysis.

The bases of the FT are time-unlimited sinusoidal waves; they extendfrom −∞ to +∞. Also sine waves are predictable and smooth, as comparedto wavelet functions which tend to be rough and anti-symmetric.

While the FT is a process of decomposing a signal into sine waves ofdifferent frequencies, the WT decomposes the signal into shifted andscaled versions of the original (or mother) wavelet. Since a wavelet isan irregular (or anti-symmetric) wave, it is better suited for analyzingsignals with local singularities (or sharp edges) than the more regularsinusoids.

A wavelet is represented by a mathematical function that divides a givenfunction or continuous-time signal into different frequency components.A wavelet is generated from a single mathematical function called amother wavelet (as shown in FIG. 3 for Gaussian wavelets), which is afinite-length or fast-decaying oscillating waveform both in time and infrequency. Mother wavelets also include some special properties such astheir integer translations and dyadic dilations, which form anorthogonal basis for the energy-limited signal space. Daughter waveletsare scaled and translated (t) copies of the mother wavelet. WTs haveadvantages over traditional FTs for representing functions that havediscontinuities and sharp changes (as inherent in user data). Moreover,wavelet transforms provide a means for accurately deconstructing andreconstructing finite, non-periodic and/or non-stationary signals, whichFTs usually cannot do.

The Continuous Wavelet Transform (CWT) of a signal, s(t), is defined asthe sum over all times of the signal multiplied by scaled and shiftedversions of a mother wavelet function ψ(t). Mathematically, the CWT of afinite energy signal, s(t), is defined as:

${{C( {a,b} )} - {\int_{R}{{s(t)}\frac{1}{\sqrt{a}}{\psi ( \frac{t - b}{a} )}{t}}}},{a \in R^{+}},{b \in R},{s \in {L^{2}(R)}}$

where C(a, b) are the continuous wavelet transform coefficients and a isa positive scaling parameter, and b denotes the amount of time-shift, asdiscussed in I. Daubechies, Ten Lectures on Wavelets, 1st ed. SIAM, 1992as, herein incorporated in its entirety by reference. The result of thistransformation is a scale-position or scale-time representation C(scale,tame). The inverse CWT can be used to recover the original signal s(t).To recover the original signal from its CWT coefficients, the InverseContinuous Wavelet Transform is used, and is defined by:

${{s(t)} = {\frac{1}{K_{\psi}}{\int_{R^{+}}{\int_{R}{{C( {a,b} )}\frac{1}{\sqrt{a}}{\psi ( \frac{t - b}{a} )}\frac{{da}\mspace{14mu} {db}}{a^{2}}}}}}},$

where K_(ψ) is a constant depending on ψ.

It is important to understand the difference between the CWT and itsdiscrete counter-part, the Discrete Wavelet Transform (DWT). The CWT canoperate at any arbitrary scale. We can control the range of scales atwhich we would like to compute wavelet coefficients. The scales canrange from one up to some maximum value determined depending on thelevel of details needed and the application of interest. In contrastwith the CWT, the Discrete Wavelet Transform (DWT) calculates waveletcoefficients at specific set of scales. When the scales and positionsare expressed as powers of two, we call these dyadic scales and dyadicpositions. In this way, DWT is less computationally expensive than theCWT, yet as accurate. Mathematically, it can be defined afterdiscretizing Equation 0 by limiting a and b to a discrete lattice(a=2^(j), b=k2^(j), (j,k)εZ²):

C(j,k)∫_(R) s(t)ψ_(j,k)(t)dt,(j,k)εZ ² ,sεL ²(R)

where C(j, k) are the discrete wavelet transform coefficients.ψ_(j,k)(t) are the wavelet basis functions or wavelet expansionfunctions, which are related to the original mother wavelet functionψ(t) as follows:

ψ_(j,k)(t)=2^(−j/2)ψ(2^(−j) t−k)

where j and k are the dilation and translation parameters, respectively.To reconstruct the original signal, the Inverse Discrete WaveletTransform (IDWT) is given by:

${s(t)} = {\sum\limits_{j \in z}{\sum\limits_{k \in z}{{C( {j,k} )}{{\psi_{j,k}(t)}.}}}}$

An efficient scheme for implementing the wavelet transform using filterswas introduced in S. G. Mallat, “A theory for multiresolution signaldecomposition: the wavelet representation,” IEEE Transactions on PatternAnalysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, July1989, herein incorporated in its entirety by reference, and isclassically known as a two-channel subband coder as discussed in G.Strang and T. Nguyen, Wavelets and Filter Banks, 2nd ed. WellesleyCollege, 1996, p. 520, herein incorporated in its entirety by reference.This method provides a fast implementation of the wavelet transform. Thewavelet decomposition is composed of low-pass and high-pass filters. Thesignal of interest is fed into both of these filters. The output of thefilters is followed by dyadic decimation. Finally, the resultingcoefficients are called approximations and details, respectively. Theapproximation coefficients (that correspond to the low-pass filter) arethe high-scale, low-frequency components of the input signal, whereasthe detail coefficients (that correspond to the high-pass filter) arethe low-scale high-frequency components of the input signal. The waveletdecomposition at the first step is illustrated in FIG. 20.

In FIG. 20, the input signal s is fed into the two complementary filtersand the outputs are the approximation coefficients, cA₁, and the detailcoefficients, cA₂. The wavelet decomposition can be continuediteratively where at each level of decomposition; the approximations aredecomposed into the next level's approximation and detail coefficients.This process leads to the analysis of the signal by decomposing it intoseveral low resolution components and can be represented as the waveletdecomposition tree shown in FIG. 21.

As mentioned before, non-stationary signals can be best dealt with thewavelet transform. In addition to that, an attractive property of the WTis its ability to perform local analysis of a larger signal, and todetect singularities (discontinuities) in the signal. This property ofWT can be used in edge detection as discussed in S. Mallat and S. Zhong,“Characterization of signals from multiscale edges,” IEEE Transactionson Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp.710-732, July 1992, herein incorporated in its entirety by reference.

The primary users (PUs) (11, 12, 13, 14, and 15 in FIG. 1) are onlyactive within certain time intervals. The no-activity gaps betweenactive intervals are referred to as spectrum holes. If such spectrumholes can be detected efficiently, then these can be used by a secondaryuser or cognitive radio user (CR) 10 resulting in better spectrumutilization. For example in FIG. 1, at time t=0, CR 10 is using thefrequency band allocated to PU 11. During the opportunistic spectrumaccess, wherein the CR 10 uses the spectrum allocated to PU 11, the CR10 must monitory when PU 11 restarts using the allocated spectrum, atwhich time CR 10 must either move to another spectrum hole, or changeoperating parameters, e.g., modulation scheme, in order to avoidinterference with the primary transmission. If neither of the previoustwo choices are available CR 10 must stop transmitting until CR 10 cantransmit without interfering with the signal of a PU. In FIG. 1, thespectrum hole becomes available at the spectrum allocated to PU 14 andCR 10 changes frequency to utilize this spectrum hole while it is notused by a PU. When PU 14 begins transmitting again, CR 10 changesfrequency the frequency band allocated to PU 12 while it is not beingused by a PU.

The Cognitive Cycle steps are: 1) Spectrum Sensing: A CR examines thetargeted frequency band(s), extracts relevant information, andidentifies possible spectrum holes; 2) Spectrum Analysis: The detectedspectrum holes are characterized and channel conditions are estimatedwithin each hole; and 3) Spectrum Decision: Based on the cognitive userrequirements, e.g., data rate and required bandwidth, the cognitiveradio determines the best available spectrum hole for the cognitive usertransmission.

While the cognitive user is transmitting over a frequency band allocatedto a PU, it is important to keep track of the changes in the radioenvironment. For example, when the current channel conditions becomeworse or when the licensed user reappears, the operation of spectrummobility comes into play, as shown in FIG. 1. During this operation, thecognitive radio switches from the current channel to some other spectrumhole, a phenomenon referred to as spectrum handoff.

From the previous discussion, it is clear that a necessary task prior todynamic spectrum access is spectrum sensing. It is the first phase inthe cognitive cycle. In this phase, efficient spectrum sensingtechniques are used to track the radio environment which may change intime and space. Several spectrum sensing methods have been discussed inthe literature with their merits and demerits. See, e.g., R. Umar and A.U. H. Sheikh, “A comparative study of spectrum awareness techniques forcognitive radio oriented wireless networks,” Physical Communication,August 2012, incorporated herein in its entirety, and T. Yucek and H.Arslan, “A survey of spectrum sensing algorithms for cognitive radioapplications,” IEEE Communications Surveys & Tutorials, vol. 11, no. 1,pp. 116-130, 2009, incorporated herein in its entirety. Spectrum sensingtechniques can be classified into two main categories, namely,transmitter detection, and interference-based detection. Wavelet basedsensing fall under the category of Energy Detection.

When the targeted frequency band is narrowband, the radio system frontend can be implemented using tunable narrowband Band-Pass Filters (BPF).However, when the spectrum utilization is high, one needs to sense awideband spectrum in order to detect efficiently spectrum whitespaces.Under this scenario, it is inefficient to install multiple narrowbandBPFs at the radio front-end to perform the sensing task. Alternatively,if only one narrowband BPF is used to scan the entire wideband(frequency range) in blocks, this becomes time consuming hence reducingthe overall performance of the cognitive radio.

Observing the fact that a wideband spectrum can be thought of as asequence of consecutive subbands, where the Power Spectral Density (PSD)within each subband is almost flat and some discontinuities exist at theboundaries of subbands. These discontinuities in the wideband PSD carrykey information about the location of boundaries and the potentialspectrum holes. A powerful mathematical tool for analyzing signal'slocal singularities is the Wavelet Transform, which can be used toextract information about edges in the signal spectrum as explained inS. Mallat and W. L. Hwang, “Singularity detection and processing withwavelets,” IEEE Transactions on Information Theory, vol. 38, no. 2, pp.617-643, March 1992, incorporated herein by reference in its entirety.In our case, edges in the wideband PSD refer to the boundaries of twoconsecutive subbands of different power levels within the wideband ofinterest. After the identification of subbands, energy is estimated foreach of these, which carries important information on spectrum holesavailable for opportunistic sharing. This idea of using WaveletTransform on the received wideband signal's PSD was first proposed in Z.Tian and G. B. Giannakis, “A Wavelet Approach to Wideband SpectrumSensing for Cognitive Radios,” in 2006 1st International Conference onCognitive Radio Oriented Wireless Networks and Communications, 2006, pp.1-5, incorporated herein by reference in its entirety.

As shown in FIG. 2, wireless signals from the licensed users shall existwithin a wide band of interest in assigned non-overlapping frequencybands with possibly non-similar powers. In the wide band of interest,there are discontinuities in the PSD at the edges of the assignedfrequency bands. A cognitive user, without prior knowledge of thenumber, bandwidth, or locations of the assigned frequency bands, canidentify the frequency band edges by convolving together the PSD andwavelet functions in the frequency domain.

In FIG. 2, the radio signal received at the CR has N frequency bands inthe interval [f₀,f_(N)] being sensed by the cognitive user. Thecognitive user must first identify the frequency bands assigned toprimary users by identifying discontinuities in the PSD at frequenciesf₁<f₂< . . . <f_(N−1). Next the cognitive user defines each subband suchthat the n^(th) subband is given by B_(n)=[f_(n−1),f_(n)]. The PSD as afunction of frequency is given by S_(r)(ƒ). After identifying thesubband frequency intervals, {f_(n)}_(n=1) ^(N−1), the PSD level withineach subband is averaged to obtain β_(n).

The wavelet smoothing function is given by φ(ƒ), and FIG. 3 shows anon-limiting example of φ(ƒ) using a to be a Gaussian wavelet. Thedilation of the wavelet smoothing function φ(ƒ) by a scale factor s isgiven by:

${\phi_{s}(f)} = {\frac{1}{s}{\phi ( \frac{f}{s} )}}$

The CWT of S_(r)(ƒ) is defined as the convolution of the observed signalPSD with the wavelet function:

W _(s) S _(r)(ƒ)=S _(r)*φ_(s)(ƒ).

W_(s)S_(r)(ƒ) provides information on the local structure of S_(r)(ƒ),such that taking the derivative of W_(s)S_(r)(ƒ) and looking for theextrema will give the largest averaged discontinuities in the PSD. Thisoperation is expressed mathematically as:

${W_{s}^{\prime}{S_{r}(f)}} = {s\frac{\;}{f}( {S_{r}*\phi_{s}} ){(f).}}$

So, the local modulus maxima W_(s)′S_(r)(ƒ) represent the edges in thePSD S_(r)(ƒ). More formally, the identification of frequency boundaries{f_(n)}_(n=1) ^(N−1) can be expressed as:

{circumflex over (f)} _(n)=maxima_(f) {|W _(s) ′S _(r)(ƒ)|},fε[f ₀ ,f_(N)].

Dyadic scales will be used (i.e., s=2^(j), j=1, 2, . . . , J.) as anon-limiting example of scale factors.

FIG. 3 shows an example of a wavelet smoothing function. FIG. 4 shows aflow chart for the basic wavelet transform method 310 for determiningboundaries between frequency bands. As discussed above the methodincludes a first step of acquiring a time domain signal 311. The secondstep is estimating the power spectral density (PSD) 312. The third stepis calculating the wavelet coefficients 313, and the final step issolving for discontinuities in the PSD 314.

The above basic method can be improved by taking advantage of the uniqueinformation provided by different dyadic scales. Small dyadic scales canresolve narrow band features but are susceptible to misidentifying highfrequency noise as the edge of a frequency band. In contrast, largedyadic scales are not susceptible to high frequency noise but alsosmooth out narrow band features. Taking the product of CWT of S_(r)(ƒ)for multiple dyadic scales suppresses the noise-induced spurious localmaxima, which are random at each scale. This multi-scale product isdefined as:

${U_{J}{S_{r}(f)}} = {\prod\limits_{j = 1}^{J}\; {W_{s = 2^{j}}^{\prime}{{S_{r}(f)}.}}}$

The method provides the estimation of frequency edges {f_(n)} ofinterest, by picking the maxima of the multi-scale product in 0. Thenoise-induced spurious local maxima of |W_(s)′S_(r)(ƒ)| are random atevery scale and tend not to propagate though all J scales; hence, theydo not show up as the local maxima of |U_(J)S_(r)(ƒ)| and peaks areenhanced due to edges while noise is suppressed:

{circumflex over (f)} _(n)=maxima_(f) {|U _(J) S _(r)(ƒ)|},fε[f ₀ ,f_(N)].

FIG. 4 shows a flow chart for the multi-scale-product method 320 ofdetermining boundaries of frequency bands allocated to PU using wavelettransform coefficients. As discussed above the method includes a firststep of acquiring a time domain signal 311, a second step of estimatingthe power spectral density (PSD) 312, a third step of calculating thewavelet coefficients 313, a fourth step of calculating the multi-scaleproduct 321, and final step of solving for discontinuities in the PSD314.

After determining the frequency bands allocated to PU, the next step isto measure the energy in each frequency band and decided whether it isbeing used or if it is available for use by the CR. FIG. 6 depicts asimple block diagram of an energy detector for determining if afrequency band is being used. The observed signal x(t) is fed to aband-pass filter which limits the bandwidth to W and selects some centerfrequency f_(c). Following the BPF, squaring device and an integrator ofa certain observation interval, T, are used. Finally, the measuredenergy from the integrator is compared to a pre-threshold, λ, and adecision about the presence or the absence of the primary user is made.The value of the threshold λ depends mainly upon the noise variance.

Instead of frequency-domain analysis, one can consider the problem ofspectrum sensing in time domain. One of the most common techniques usedin time domain is Energy Detection. As mentioned before, when acognitive radio receiver does not have any prior knowledge on theprimary user's signal and the only thing that is known is the power ofthe random Gaussian noise, then the optimal solution in terms ofimplementation is an Energy Detector (ED) as discussed in A. Sahai andN. Hoven, “Some fundamental limits on cognitive radio,” AllertonConference on Comm., Control and Computing., 2004, herein incorporatedin its entirety by reference. The idea of determining the presence ofunknown deterministic signals using Energy Detector was first discussedin H. Urkowitz, “Energy detection of unknown deterministic signals,”Proceedings of the IEEE, vol. 55, no. 4, pp. 523-531, 1967, hereinincorporated in its entirety by reference. FIG. 6 depicts a simple blockdiagram of an energy detector.

The observed signal x(t) is fed to a band-pass filter which limits thebandwidth to W and selects some center frequency f_(c). Following theBPF, squaring device and an integrator of a certain observationinterval, T, are used. Finally, the measured energy from the integratoris compared to a pre-threshold, λ, and a decision about the presence orthe absence of the primary user is made. The value of the threshold λdepends mainly upon the noise variance.

The input signal x(t) can have several possible forms based on whetherthe primary user is present or absent, which we denote by hypotheses H₁,and H₀, respectively:

${x(t)} = \{ {\begin{matrix}{{n(t)},} & H_{0} \\{{{h \times {s(t)}} + {n(t)}},} & H_{1}\end{matrix},} $

where s(t) represents the primary user's signal, h is the channel gain,and n(t) is the noise.

In FIG. 6, the output of the integrator is effectively the decisionstatistic, which is represent by Y. In order to analyze the performanceof the above mentioned energy detector, the statistical distribution ofY has to be known under both hypotheses. The decision statistic Y willhave the following distributions:

$ Y \sim\{ \begin{matrix}{\chi_{2{TW}}^{2},} & H_{0} \\{{\chi_{2{TW}}^{2}( {2\gamma} )},} & H_{1}\end{matrix} $

where χ_(2TW) ² denotes a central chi-square distribution and χ_(2TW) ²(2γ) denotes a non-central chi-square distribution, both with the samedegrees of freedom, i.e., 2TW (TW is the time-bandwidth product). Thenon-central chi-square distribution has a non-centrality parameter of2γ, where γ is the receiver SNR (cognitive radio). For simplicity, wedenote the time-bandwidth product as u=TW, and assume that T and W arechosen such that u has an integer value.

FIG. 7 depicts the two regions, H₀ and H₁, separated by a singlethreshold λ. This threshold divides the decision as either present ifthe observed energy is above the threshold (hypothesis H₁ is true), orotherwise absent (hypothesis H₀ is true). The performance of theenergy-detector based spectrum sensing is established mainly on twoparameters, namely, probability of misdetection P_(m) and probability offalse alarm P_(f). If the cognitive user (CR) decides an absence whilethe primary user (PU) is present; this error is represented with theprobability of misdetection P_(m), which would cause a substantialinterference at the PU. On the other hand, if the CR decides a presencewhile the PU is absent, the cognitive user would miss a spectrum usageopportunity; a phenomenon represented by the probability of false alarmP_(f). Jointly, the probability of misdetection P_(m) and theprobability of false alarm P_(f) define what is called ComplementaryReceiver Operating Characteristics (C-ROC). Sometimes instead of P_(m),we use the probability of detection P_(d) which is related to P_(m) as1−P_(m). Probability of detection P_(d) defines the probability withwhich the CR will detect the presence of PU, given the PU is actuallyactive. These parameters can generally be evaluated as:

P _(m) =Pr(Y<λ|H ₁)

P _(f) =Pr(Y>λ|H ₀)

P _(d)=1−P _(m) =Pr(Y>λ|H ₁)

where, as before, λλ is the decision threshold. The plot of P_(d) vs.P_(f) is called Receiver Operating Characteristics (ROC).

There is always a trade-off between P_(d) (or P_(m)) and P_(f). Asillustrated in FIG. 22, we can have two distinct PDFs of a receivedsignal, corresponding to two possible hypotheses, H₀ and H₁. By varyingthe threshold, we can control the two type errors, namely, P_(m) andP_(f). If the threshold is kept excessively low, P_(m) decreases at theexpense of increased P_(f). A high P_(f) implies spectrum inefficientutilization because of high false alarms. Alternatively, if thethreshold is set needlessly high, we can reduce P_(f) at the cost ofincreasing P_(m). A high P_(m) implies a high probability of interferingwhile PU is active. Evidently, we cannot reduce both types of errorsimultaneously. The optimal approach is to use Neyman-Pearson detectoras discussed in S. M. Kay, Fundamental of Statistical Signal Processing:Detection Theory. Englewood Cliffs, N.J.: Prentice-Hall, 1998, hereinincorporated in its entirety by reference, where we constrain P_(f) to afixed value, and minimize P_(m). In other words, we fix the value ofP_(f), and try to maximize P_(d).

If we consider no fading, then h will be a constant in equation 0. Forsuch additive white Gaussian noise (AWGN) environment, the closed-formexpressions for P_(d) and P_(f) has been reported in F. F. Digham, M. S.Alouini, and M. K. Simon, “On the energy detection of unknown signalsover fading channels,” in IEEE International Conference onCommunications, 2003. ICC '03, 2003, vol. 5, pp. 3575-3579, hereinincorporated by reference in its entirety, as:

P _(dAWGN) =Q _(u)(√{square root over (2γ)},√{square root over (λ)})

where Q_(u)(a, b) is the generalized Marcum Q-function as discussed inA. Nuttall, “Some integrals involving the Q_M function (Corresp.),” IEEETransactions on Information Theory, vol. 21, no. 1, pp. 95-96, January1975, herein incorporated by reference in its entirety, and

$P_{f} = \frac{\Gamma ( {u,\frac{\lambda}{2}} )}{\Gamma (u)}$

where Γ(.,.) and Γ(.) are the incomplete and complete gamma function,respectively.

For the case where we assume the channel fading h to be Rayleighdistributed, only the expression for P_(d) will change. Under Rayleighfading, the signal-to-noise-ratio (SNR) γ will follow exponentialdistribution and for this case P_(d Ray) is shown to be derived as:

$P_{dRay} = {{^{- \frac{\lambda}{2}}{\sum\limits_{n = 0}^{u - 2}{\frac{1}{n!}( \frac{\lambda}{2} )^{n}}}} + {( \frac{1 + \gamma}{\gamma} )^{u - 1}\lbrack {^{- \frac{\lambda}{2{({1 + \overset{\_}{\gamma}})}}} - {^{- \frac{\lambda}{2}}{\sum\limits_{n = 0}^{u - 2}{\frac{1}{n!}\frac{\lambda \; \overset{\_}{\gamma}}{2( {1 + \overset{\_}{\gamma}} )}}}}} \rbrack}}$

where γ is the average received SNR. Since P_(f) is considered whenthere is no signal present and as such is independent of SNR γ,therefore, its expression remains the for the cases of fading andnon-fading channels.

A high P_(f) implies spectrum inefficient utilization because of highfalse alarms. Alternatively, if the threshold is set needlessly high, wecan reduce P_(f) at the cost of increasing P_(m). A high P_(m) implies ahigh probability of interfering while PU is active. Evidently, we cannotreduce both types of error simultaneously. The optimal approach is touse Neyman-Pearson detector as discussed in S. M. Kay, Fundamental ofStatistical Signal Processing: Detection Theory. Englewood Cliffs, N.J.:Prentice-Hall, 1998, herein incorporated by reference in its entirety,where we constrain P_(f) to a fixed value, and minimize P_(m). In otherwords, we fix the value of P_(f), and try to maximize P_(d).

As with any wireless communication system, the performance degrades inmultipath fading channels. One way to overcome the effects of multipathfading is to use multiple antennas to improve performance as discussedin S. M. Alamouti, “A simple transmit diversity technique for wirelesscommunications,” IEEE Journal on Selected Areas in Communications, vol.16, no. 8, pp. 1451-1458, 1998, herein incorporated in its entirety byreference. Similarly, fading in wireless channels creates uncertainty inthe SNR at the CR receiver input, making it difficult for the CR toprovide a reliable decision about the absence or presence of the PU,since when the CR is experiencing a deep fading or shadowing due tolarge obstacles over the primary-to-secondary channel, the amount ofenergy observed during a fixed time-bandwidth product may not be enoughto decide about the presence of a PU. One way to overcome this problemis to increase the amount of local processing which, in the case ofenergy detector, translates into increasing the time-bandwidth product.However, this is not always possible due to constraints of the sensingperiod set by the regulator.

Rather than increasing the time-bandwidth product, the cognitive usercan cooperate with neighboring cognitive users as discussed in G.Ganesan, Y. Li, and S. Li, “Spatiotemporal Sensing in Cognitive RadioNetworks,” in 2007 IEEE 18th International Symposium on Personal, Indoorand Mobile Radio Communications, 2007, pp. 1-5, herein incorporated inits entirety by reference. Since the multipath fading statisticsfluctuates considerably on the scale of a fraction of wavelength andshadowing fluctuates considerably on the scale of 20-500 m based on thenature of environment, it is highly unlikely that multiple cooperatingCRs will experience deep fade and/or large obstacles at the same time asdiscussed in J. Ma, G. Y. Li, and B. H. Juang, “Signal processing incognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823,2009, herein incorporated in its entirety by reference, F. F. Digham,M.-S. Alouini, and M. K. Simon, “On the Energy Detection of UnknownSignals Over Fading Channels,” IEEE Transactions on Communications, vol.55, no. 1, pp. 21-24, January 2007, herein incorporated in its entiretyby reference, and I. F. Akyildiz, B. F. Lo, and R. Balakrishnan,“Cooperative spectrum sensing in cognitive radio networks: A survey,”Physical Communication, vol. 4, no. 1, pp. 40-62, March 2011, hereinincorporated in its entirety by reference.

The cooperation between multiple CRs can be carried in either acentralized or a distributed fashion as shown in FIG. 8 and FIG. 9. FIG.8 shows cognitive users CR1 20, CR2 30, CR3 40, CR4 50, and CR5 60reporting measurement results to a centralized node CR0 70 called thefusion center (FC). In contrast, FIG. 9 shows distributed network ofcognitive users, where each CR operates as its own FC. In both cases theFC operates in a nearly identical manner. Thus the essentiallydifference between distributed and centralized network architectures isthe location of the FC, not the function of the FC. For simplicity wediscuss only the centralized cooperation system of CRs, but the resultsare equally applicable to a distributed cooperation system of CRs.

When a centralized fusion center (CR0 70 in FIG. 8) is used to handlethe different cognitive decisions, the cooperative spectrum sensing canbe performed in the following manner: 1) All the cooperating cognitiveusers start by sensing a targeted band independently; 2) Eachcooperating node would forward either its local binary decision or itcan just send its observation value directly to the fusion center (FC)70 over the reporting channel 19; 3) Finally, the fusion center 70 fusesall the received data (or decisions) to infer the presence or absence ofthe PU 20. The fusion center 70 can also be referred to as commonreceiver, master node, base station, combining node, and designatedcontroller. As shown in FIG. 8, CR0 is the FC while CR1-CR5 (20, 30, 40,50, and 60) are the cooperating CRs. When using cooperation amongmultiple CRs for spectrum sensing, certain protocols need to be definedfor the purpose of sharing sensing information over the reportingchannel 19. In contrast to the reporting channel 19, the physicalpoint-to-point connection between the PU and a CR for the purpose ofsensing the primary transmitter's signal is called a sensing channel 18.Different architecture have been proposed for reporting channels, e.g.using ISM band and ultra wide band (UWB) have been discussed in C. Guo,T. Zhang, Z. Zeng, and C. Feng, “Investigation on Spectrum SharingTechnology Based On Cognitive Radio,” in 2006 First InternationalConference on Communications and Networking in China, 2006, pp. 1-5, andJ. Perez-Romero, O. Salient, R. Agusti, and L. Giupponi, “A NovelOn-Demand Cognitive Pilot Channel Enabling Dynamic Spectrum Allocation,”in 2007 2nd IEEE International Symposium on New Frontiers in DynamicSpectrum Access Networks, 2007, pp. 46-54. A simple protocol using timedivision multiple access (TDMA) to share the sensing information withthe fusion center is proposed in P. Pawelczak, C. Guo, R. V. Prasad, andR. Hekmat, “Clusterbased spectrum sensing architecture for opportunisticspectrum access networks,” in IEEE Vehicular Technology ConferenceVTC2007, 2007, where the cooperating CRs are divided into clusters basedon their geographical location and send their sensing data to theparticular cluster head only during the assigned time slots.

It is very important to consider that the cooperation mechanism shouldhave as low as possible overhead, and it should be robust to networkchanges and failures. Also, the amount of delay needs to be minimizedfor a particular cooperation algorithm. Usually, such type of protocolsare defined at Medium Access Layer (MAC) as discussed in L. Musavian andT. Le-Ngoc, “Cross-layer design for cognitive radios with joint AMC andARQ under delay QoS constraint,” in 2012 8th International WirelessCommunications and Mobile Computing Conference (IWCMC), 2012, pp.419-424, herein incorporated in its entirety by reference.

Based on whether the CRs are sending their 1-bit binary decision ortheir observation value to the fusion center, the combination is calledeither decision fusion or data fusion, respectively. Sometimes the termshard combination and soft combination are used instead of using therespective terms decision fusion or data fusion.

FIG. 10 shows a proposed cooperative spectrum sensing framework from I.F. Akyildiz, B. F. Lo, and R. Balakrishnan, “Cooperative spectrumsensing in cognitive radio networks: A survey,” Physical Communication,vol. 4, no. 1, pp. 40-62, March 2011, herein incorporated in itsentirety by reference. The framework consists of the PU, cooperatingCRs, FC, the RF channels (sensing and reporting channels), and anoptional remotely located database. As shown in the framework, a groupof collaborative CRs, presumably independent of each other, performtargeted sensing using their RF frontend 21. The processing unit, 22 ofCR1 20 may include, at least, a signal processor 23, data fusion 24, andhypothesis testing 25 entities. The RF frontend 21 is capable to beconfigured for data transmission or local sensing. Besides that,analog-to-digital conversion will also be done by the RF frontend 21.The local observations of the cooperating CRs (20, 30, and 40) candirectly be transmitted to the FC 70, or it can be locally processed toprovide a decision to the FC 70. Usually, certain amount of processingon the local observations is needed to minimize the bandwidthrequirement over the reporting channels. The processing may include theevaluation of the energy statistics and thresholds. When the localdecision or the observations are ready, a request to a higher layer(e.g., MAC layer) is sent to acquire the access of a control channel.The FC 70 in the centralized CSS framework 100 is a powerful cooperatingCR which has all the capabilities as the other CRs. In addition, the FC70 has other functionalities, such as user selection and knowledge base,to undertake the cooperation tasks successfully. Based on therequirement and the ability of the FC 70, the FC 70 can be connected toan external (remotely located) database 81 through an ultra-high speedcommunication medium 82 (e.g., fiber optics). This external databasewill assist the FC and can provide information regarding the PU 20activity and white spaces.

When decision-fusion is used, each CR compares its observed energy valuewith pre-fixed threshold λ, if the observed value is greater than λ, thereported decision is 1 (H₁), while the reported decision is 0 (H₀) ifthe value is less than the threshold. After collecting L local 1-bitdecisions, the fusion center makes an occupancy-decision based on acertain decision-fusion rule, which can be represented as

$Z = {\sum\limits_{i = 1}^{L}{D_{i}\{ {\begin{matrix}{{\geq K},} & H_{1} \\{{< K},} & H_{0}\end{matrix},} }}$

As discussed in K. Ben Letaief, “Cooperative Communications forCognitive Radio Networks,” Proceedings of the IEEE, vol. 97, no. 5, pp.878-893, May 2009, herein incorporated by reference in its entirety.

If there exists at least K out of L CRs having their local observationvalues above the pre-fixed thresholds, then the fusion center will inferpresence of the PU, i.e., H₁, otherwise the fusion center will declarethat there is no PU signal transmitted, i.e, H₀. Such decision criterionis also called K-out-of-L rule as discussed in P. K. Varshney,Distributed Detection and Data Fusion. New York: Springer-Verlag, 1997,p. 299, herein incorporated in its entirety by reference. It was shownin A. Ghasemi and E. S. Sousa, “Spectrum sensing in cognitive radionetworks: the cooperation-processing tradeoff,” Wireless Communicationsand Mobile Computing, vol. 7, no. 9, pp. 1049-1060, November 2007,herein incorporated in its entirety by reference, that under the case ofdistributed individual and independent decisions, the optimum (in termsof detection performance) decision-fusion rule is 1-out-of-L rule (i.e.,OR rule). Therefore, in the rest of the thesis we shall resort to the ORrule as our final decision-fusion rule. Instead of calculatingindividual thresholds for each cooperating user, for simplicity, it isassumed that all collaborative cognitive users have the same decisionrule (i.e., same threshold λ), according to some fixed cooperativeprobability of false-alarm, Q_(f) as discussed in A. Ghasemi and E. S.Sousa, “Collaborative spectrum sensing for opportunistic access infading environments,” in First IEEE International Symposium on NewFrontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005, pp.131-136, herein incorporated in its entirety by reference.

FIG. 11 shows a flow chart of the hard decision time domain method 420for a cooperative spectrum sensing network of CRs to determine whether afrequency band allocated to PUs is being used. The method includes afirst step of calculating the energy in the frequency band 411, a secondstep of determining the received energy value 412, a third step ofmaking a hard decision about whether the frequency band is used 421, afourth step of transmitting the CR result to a FC 413, a fifth step ofthe FC combining results from multiple CRs to obtain a final decision422, and a final step of transmitting the final decision to the CRs 415.

Alternatively to the decision fusion for hard decisions discussed above,the fusion center can also exploit the diversity provided by using adata-fusion criterion to determine the occupancy state of the targetedband. In data-fusion, each CR simply reports their original sensing datato the fusion center. Although, data-fusion imposes large amount ofcommunication overhead over the control channel, but it has excellentdetection performance as discussed in J. Ma, G. Y. Li, and B. H. Juang,“Signal processing in cognitive radio,” Proceedings of the IEEE, vol.97, no. 5, pp. 805-823, 2009, herein incorporated in its entirety byreference. A data-fusion based cooperative spectrum sensing method wasproposed in S. Haykin, “Cognitive radio: brain-empowered wirelesscommunications,” IEEE Journal on Selected Areas in Communications, vol.23, no. 2, pp. 201-220, February 2005, herein incorporated in itsentirety by reference, which he called it as multitaper-methodsingular-value-decomposition (MTM-SVD). In the MTM-SVD, the Lcooperating CR users cooperatively estimate the interference temperatureof the radio environment. As discussed in D. J. Thomson, “Spectrumestimation and harmonic analysis,” Proceedings of the IEEE, vol. 70, no.9, pp. 1055-1096, 1982, herein incorporated in its entirety byreference, each cooperating CR applies mutitaper method to analyze thespectrum by first computing its k^(th) eigenspectrum for the targetedband as:

${{Y_{k\;}^{(l)}(f)} = {\sum\limits_{n = 1}^{N}{{w_{k}(n)}{y_{l}(n)}^{{- }\; \omega \; n}}}},{1 \leq k \leq K}$

where y_(l)(n) are the observed samples at the l^(th) CR, and w_(k)(n)represents the k^(th) Slepian sequence (discussed in D. Slepian,“Prolate spheroidal wave functions, Fourier analysis and uncertainty,”Bell Syst. Tech. J., vol. 57, pp. 1371-1430, 1978, herein incorporatedthat each CR is to send its eigenspectrum vector

Y _(l)(ƒ)=(Y ₁ ^((l))(ƒ),Y ₂ ^((l))(ƒ), . . . ,Y _(K) ^((l))(ƒ)),1≦l≦L

to the fusion center. Based on such vectors from each of the Lcooperating CRs, the fusion center computes an L×K eigenspectrum matrixas:

${A(f)} = \begin{bmatrix}{w_{1}{Y_{1}^{(1)}(f)}} & {w_{1}{Y_{2}^{(1)}(f)}} & \ldots & {w_{1}{Y_{K}^{(1)}(f)}} \\{w_{2}{Y_{1}^{(2)}(f)}} & {w_{2}{Y_{2}^{(2)}(f)}} & \ldots & {w_{2}{Y_{K}^{(2)}(f)}} \\\vdots & \vdots & \ddots & \vdots \\{w_{L}{Y_{1}^{(L)}(f)}} & {w_{L}{Y_{2}^{(L)}(f)}} & \; & {w_{M}{Y_{K}^{(L)}(f)}}\end{bmatrix}$

where w_(l) are the weights of l^(th) CR which is computed after takinginto consideration the instantaneous environment information intoaccount. Each row in A(ƒ) corresponds to the eigenspectrum vector from aparticular CR. If the primary user is present, the eigenspectrum vectorconsists of the PU signal plus noise. The noise is independent for thedistributed CRs, while there will be a correlation in the PU signalpart. Observing this fact, the MTM-SVD scheme exploits the correlationdue to the PU signal by applying SVD to the eigenspectrum matrix 0:

${A(f)} = {\sum\limits_{k = 1}^{K}{{\sigma_{k}(f)}{u_{k}(f)}{v_{k}^{H}(f)}}}$

where σ_(k) (ƒ) is the k^(th) singular value of A(ƒ), u_(k)(ƒ) and ν_(k)(ƒ) are the associated left and right singular vectors, respectively.Finally, the fusion center takes the spectrum occupancy decision basedon the largest singular value of the matrix A(ƒ). This method (MTM-SVD)provides a means for cooperative spectrum sensing to estimate thepresence or absence of the primary user with high accuracy as discussedin J. Ma, G. Y. Li, and B. H. Juang, “Signal processing in cognitiveradio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823, 2009,herein incorporated in its entirety by reference.

For the MTM-SVD scheme described above, the complexity of the wholeprocedure is quite high. Not only sending the K-dimensional vector fromeach CR to the fusion center would increase lots of communication burdenover the reporting channel, but the SVD operation on the matrix A(ƒ) isalso computationally very expensive.

Eigenvalue based cooperative spectrum sensing has also been proposed inS. Xu, Y. Shang, and H. Wang, “Eigenvalues based spectrum sensingagainst untrusted users in cognitive radio networks,” in 2009 4thInternational Conference on Cognitive Radio Oriented Wireless Networksand Communications, 2009, pp. 1-6, herein incorporated in its entiretyby reference. This method uses the eigenvalue based approach originallyproposed in Y. Zeng, C. L. Koh, and Y.-C. Liang, “Maximum EigenvalueDetection: Theory and Application,” in 2008 IEEE InternationalConference on Communications, 2008, pp. 4160-4164, herein incorporatedin its entirety by reference. Observing the fact that the statisticalcovariance matrix of the observed signal will have differentcharacteristics based on whether the PU is present or not, it has beenproposed that an eigenvalue decomposition based approach. In thisapproach, the sample covariance matrix is computed from the observedsignal's samples. Then the maximum eigenvalue (MEV) of the samplecovariance matrix is calculated and the value is compared with athreshold to decide about the spectrum availability. This approach hasbeen used in a cooperative fashion where each cooperating CR userperforms the eigenvalue decomposition of the sample covariance matrix,and the MEV is computed. This MEV is compared with prefixedtwo-thresholds to decide about the reliability of the cooperating CRs.The CRs with reliable decision sends their decision to the fusioncenter, where the non-reliable ones send directly their MEVs to thefusion center. Finally, the fusion center fuses all the data to decideabout the occupancy state of the spectrum. Although, the eigenvaluebased spectrum sensing technique provides very good results without anyprior knowledge about the channel, noise power, or PU signal, but thewhole decomposition process is quite computationally expensive. Also theuse of the random matrix theory to set the threshold values makes itdifficult to obtain the accurate closed form expression for thethresholds.

Various soft-combination schemes with low-complexity have been discussedin J. Ma, G. Zhao, and Y. Li, “Soft Combination and Detection forCooperative Spectrum Sensing in Cognitive Radio Networks,” IEEETransactions on Wireless Communications, vol. 7, no. 11, pp. 4502-4507,November 2008, herein incorporated in its entirety by reference. Inthese schemes, each CR reports the value of the received energy to thefusion center, and the fusion center takes a decision based on a certaindata-fusion (combining) criterion (or diversity combining) rule asdiscussed in A. Pandharipande and J.-P. M. G. Linnartz, “PerformanceAnalysis of Primary User Detection in a Multiple Antenna CognitiveRadio,” in 2007 IEEE International Conference on Communications, 2007,pp. 6482-6486, herein incorporated in its entirety by reference. In D.Brennan, “Linear Diversity Combining Techniques,” Proceedings of theIRE, vol. 47, no. 6, pp. 1075-1102, June 195, herein incorporated in itsentirety by reference, it was shown that, under the case of independentdiversity branches, the optimum combining scheme is Maximal RatioCombining (MRC). However, MRC requires full channel knowledge (amplitudeand phase) for all branches. In MRC reception, the received signals{x_(l) (t)}_(l=1) ^(L), where L is the number of diversity branches, arefirst co-phased, weighted proportionately to their channel gain and thensummed up to yield a new signal x_(MRC)(t)=Σ_(l=1) ^(L) h_(l)*x_(l)(t),where h_(l) is the channel coefficient of the l^(th) diversity branch. Aless complex scheme is the traditional Equal Gain Combining (EGC), whichdoesn't require channel fading amplitudes estimation, and, under thecase of identical and independent diversity branches, provides acomparable detection performance to that of MRC as discussed in S. P.Herath, N. Rajatheva, and C. Tellambura, “Energy Detection of UnknownSignals in Fading and Diversity Reception,” IEEE Transactions onCommunications, vol. 59, no. 9, pp. 2443-2453, September 2011, hereinincorporated in its entirety by reference, and A. Ghasemi and E. S.Sousa, “Opportunistic Spectrum Access in Fading Channels ThroughCollaborative Sensing,” Journal of Communications, vol. 2, no. 2, pp.71-82, March 2007, herein incorporated in its entirety by reference. InEGC reception the received signals {x_(l)(t)}_(l=1) ^(L), where L is thenumber of diversity branches, are co-phased only in each branch and thensummed up to yield a new signal x_(EGC)(t)=Σ_(l−1) ^(L)e^(−jφ) ^(l)x_(l)(t), where φ_(l) is the phase of the l^(th) diversity branch. Sincethe difference between MRC and EGC is not very large in terms ofperformance, but in terms of complexity, MRC is more complex than EGC,therefore we shall resort to EGC as our data-fusion rule and assume thata base station has the necessary information to perform EGC of receivedenergy detector outputs.

FIG. 12 shows a flow chart of the soft decision time domain method 410for a cooperative spectrum sensing network of CRs to determine whether afrequency band allocated to PUs is being used. The method includes afirst step of calculating the energy in the frequency band 411, a secondstep of determining the received energy value 412, a third step oftransmitting the CR result to a FC 413, a fourth step of the FCcombining results from multiple CRs to obtain a final decision 422, anda final step of transmitting the final decision to the CRs 415.

FIG. 23 and FIG. 24 show simulation results for a network of ten CRsusing the decision fusion (the OR rule and indicated in the figures bythe diamond symbol) and using data fusion (EGC and indicated in thefigures by the circle symbol). As discussed above, the performancedegradation under fading environments can be mitigated by the use ofmultiples cooperating CR nodes. Below we will show the simulationresults under additive white Gaussian noise (AWGN) and Rayleigh fadingenvironments which shows the performance gain in combining tencooperating CRs and using either data- or decision-fusion techniques. Asdiscussed in A. Ghasemi and E. S. Sousa, “Opportunistic Spectrum Accessin Fading Channels Through Collaborative Sensing,” Journal ofCommunications, vol. 2, no. 2, pp. 71-82, March 2007, hereinincorporated by reference in its entirety, it has been shown that 10cooperating users are sufficient enough to: 1) Provide high detectionperformance while keeping the probability of false-alarm extremely low,2) Lower the required observation time and bandwidth, 3) Lower therequired received SNR value, 4) Mitigate the fading effects.

The decision fusion (OR rule) approach requires fewer bits over thereporting channel (1-bit per user). On the other hand, when data fusionEGC is used, more feedback bits are required (m-bits per user, m≧1m≧1),which sacrifices the spectral efficiency. However, as shown in thesimulation results above for cooperative spectrum sensing, data fusionoutperforms decision fusion. Therefore, as can be seen from the above,we have a very clear tradeoff between performance and number of bits.One improvement of the hybrid data-decision method is that it minimizescommunication bandwidth similar to data fusion while maintaining theperformance of data fusion by employing a bi-threshold detector thatswitches between hard decisions (decision fusion) and soft decisions(data fusion) depending on the magnitude of the signal. When all CRs areequipped with bi-threshold detectors the network of CRs will self-selectinto a set of CRs with binary decisions and another set of CRs providingenergy measurements, but not decisions, to the fusion center. Becausemany CRs provide decisions, requiring significantly less data bereported to the fusion center, the hybrid data-decision fusion methodcan substantially reduce the overall number of sensing bits over thereporting channel at the expense of a negligible loss in performancecompared to EGC. Also, in contrast to the bi-threshold detector in C.Sun, W. Zhang, and K. Ben Letaief, “Cooperative Spectrum Sensing forCognitive Radios under Bandwidth Constraints,” in 2007 IEEE WirelessCommunications and Networking Conference, 2007, pp. 1-5, hereinincorporated by reference in its entirety, which are used to performonly decision fusion, the hybrid data-decision fusion method exploitsthe information of those CRs sending soft decisions in order to improvethe performance.

SUMMARY OF THE INVENTION

The foregoing paragraphs have been provided by way of generalintroduction, and are not intended to limit the scope of the followingclaims. The described embodiments, together with further advantages,will be best understood by reference to the following detaileddescription taken in conjunction with the accompanying drawings.

In one embodiment, the present disclosure provides a robust andefficient method for spectrum sensing to detect spectrum holes byestimating the power spectral density (PSD) of a received signal andfinding the boundaries between allocated frequency subbands within awideband of interest. The boundaries are found by detectingdiscontinuities in the the PSD. A wavelet transform technique is used todetect PSD discontinuities by convolving the first derivative of waveletsmoothing functions with the PSD and identifying the local maxima of theconvolved signal as edges in the PSD corresponding to boundaries betweensubbands. Here, the convolved signal is referred to as the wavelettransform coefficients, although it differs from a more traditionalnotion of the wavelet transform being a convolution with waveletsmoothing function in the absence of any derivatives.

The method of identifying subband edges is improved by suppressing thenoise effects. Noise can create spurious local maxima in the wavelettransform coefficients that will be confused for subband edges. Wavelettransform coefficients with different scale factors tend to haveuncorrelated spurious noise coefficients, whereas the wavelet transformcoefficients corresponding to genuine subband edges tend to be highlycorrelated across scale factors. Therefore, forming a single multi-scalecoefficient by combining multiple wavelet transform coefficients ofdifferent scale factors minimize coefficients attributable to noisewhile maximizing coefficients attributable to subband edges.Additionally, to further minimize spurious noise coefficients, a noisefloor is determined for the multi-scale coefficient and is used indefining a multi-scale coefficient noise threshold. Multi-scalecoefficients below this threshold are then suppressed such that theywill not be misidentified as subband edges.

After finding the subbands within the wideband of interest, a decisionis made about whether each subbands is being used by a primary users oris available to secondary users (e.g. cognitive radio users). Thisdecision is made by detecting the energy within the subband andcomparing the energy to a threshold, and signaling the frequency bandavailability based on the comparison.

In another aspect, the disclosure provides that the defining of a noisethreshold and suppressing coefficients below this threshold can also beused on the raw wavelet transform coefficients before combining thewavelet transform coefficients to form the multi-scale coefficients.

In another aspect, the disclosure provides that the unwanted effects ofnoise can further be suppressed by medium filtering the PSD beforecalculating the wavelet transform coefficients.

In another aspect, the disclosure provides a bi-threshold energydetector with a higher threshold and a lower threshold to decide whetherthe frequency band is available to cognitive radio users. When thesignal is less than both thresholds the decision is a hard decision thatthe frequency band is available. When the signal is greater than boththresholds the decision is a hard decision that the frequency band isnot available. When the signal is greater than the lower threshold andless than the the higher threshold, then decision is a soft decision andbi-threshold detector reports a signal proportional to the receivedenergy value for the frequency band.

In another aspect the disclosure provides a fusion center to receivehard decisions and soft decisions from a cooperative spectrum sensingnetwork of cognitive radio users, where the cognitive radio users areequipped with bi-threshold energy detectors. The fusion center performsdata fusion on the soft decision, such that the soft decisions for eachfrequency band are combined into a cooperative soft decision. The fusioncenter performs data fusion on the hard decision, such that the harddecisions for each frequency band are combined into a cooperative harddecision. For each frequency band, the fusion center combines the softcooperative decision and the hard cooperative decision to obtain a finaldecision and signal frequency band availability.

In another aspect the disclosure provides that the fusion centerperforms data fusion on the hard decisions from the network of cognitiveradio users by deciding that if all of the hard decisions are that thefrequency band is available, then the cooperative hard decision is thatthe frequency band is available to cognitive radio users, and otherwisethe cooperative hard decision is that the frequency band is notavailable. The fusion center also performs decision fusion on the softdecisions from the network of cognitive radio users by linear combiningthe reported received energy values from cognitive radio users makingsoft decision, and when the linear combination of received energy valuesis less than a cooperative soft decision threshold, then the cooperativesoft decision is that the frequency band is available, and otherwise thecooperative soft decision is that the frequency band is not available.

In one embodiment, the present disclosure provides a robust andefficient method for spectrum sensing to detect spectrum holes byestimating the power spectral density (PSD) of a received signal andfinding the boundaries between allocated frequency subbands within awideband of interest. The boundaries are found by detectingdiscontinuities in the the PSD. A wavelet transform technique is used todetect PSD discontinuities by convolving the first derivative of waveletsmoothing functions with the PSD and identifying the local maxima of theconvolved signal as edges in the PSD corresponding to boundaries betweensubbands. Here, the convolved signal is referred to as the wavelettransform coefficients, although it differs from a more traditionalnotion of the wavelet transform being a convolution with waveletsmoothing function in the absence of any derivatives.

The method of identifying subband edges is improved by suppressing thenoise effects. Noise can create spurious local maxima in the wavelettransform coefficients that will be confused for subband edges. Wavelettransform coefficients with different scale factors tend to haveuncorrelated spurious noise coefficients, whereas the wavelet transformcoefficients corresponding to genuine subband edges tend to be highlycorrelated across scale factors. Therefore, forming a single multi-scalesum coefficient by linear combining multiple wavelet transformcoefficients of different scale factors minimize coefficientsattributable to noise while maximizing coefficients attributable tosubband edges.

After finding the subbands within the wideband of interest, a decisionis made about whether each subbands is being used by a primary users oris available to secondary users (e.g. cognitive radio users). Thisdecision is made by detecting the energy within the subband andcomparing the energy to a threshold, and signaling the frequency bandavailability based on the comparison.

In another aspect, the disclosure provides a bi-threshold energydetector with a higher threshold and a lower threshold to decide whetherthe frequency band is available to cognitive radio users. When thesignal is less than both thresholds the decision is a hard decision thatthe frequency band is available. When the signal is greater than boththresholds the decision is a hard decision that the frequency band isnot available. When the signal is greater than the lower threshold andless than the the higher threshold, then decision is a soft decision andbi-threshold detector reports a signal proportional to the receivedenergy value for the frequency band.

In another aspect, the disclosure provides a fusion center to receivehard decisions and soft decisions from a cooperative spectrum sensingnetwork of cognitive radio users, where the cognitive radio users areequipped with bi-threshold energy detectors. The fusion center performsdata fusion on the soft decision, such that the soft decisions for eachfrequency band are combined into a cooperative soft decision. The fusioncenter performs data fusion on the hard decision, such that the harddecisions for each frequency band are combined into a cooperative harddecision. For each frequency band, the fusion center combines the softcooperative decision and the hard cooperative decision to obtain a finaldecision and signal frequency band availability.

In another aspect, the disclosure provides that the fusion centerperforms data fusion on the hard decisions from the network of cognitiveradio users by deciding that if all of the hard decisions are that thefrequency band is available, then the cooperative hard decision is thatthe frequency band is available to cognitive radio users, and otherwisethe cooperative hard decision is that the frequency band is notavailable. The fusion center also performs decision fusion on the softdecisions from the network of cognitive radio users by linear combiningthe reported received energy values from cognitive radio users makingsoft decision, and when the linear combination of received energy valuesis less than a cooperative soft decision threshold, then the cooperativesoft decision is that the frequency band is available, and otherwise thecooperative soft decision is that the frequency band is not available.

In another aspect, the disclosure provides that the unwanted effects ofnoise can further be suppressed by medium filtering the PSD beforecalculating the wavelet transform coefficients.

In another aspect, the disclosure provides that a noise threshold isdefined for the multi-scale sum coefficients and those multi-scale sumcoefficients which are less than the multi-scale noise threshold aresuppressed such that they will not be misidentified as subband edges.

In another aspect, the disclosure provides that the defining of a noisethreshold and suppressing coefficients below this threshold can also beused on the raw wavelet transform coefficients before combining thewavelet transform coefficients to form the multi-scale coefficients.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is a three axis plot showing time, frequency, and power on theaxes. The figure gives a notional example of the spectrum sensing andspectrum handoff in a cognitive radio as discussed in I. F. Akyildiz,W.-Y. Lee, M. C. Vuran, and S. Mohanty, “next generation/dynamicspectrum access/cognitive radio wireless networks: A survey,” ComputerNetworks, vol. 50, no. 13, pp. 2127-2159, September 2006.

FIG. 2 is a frequency diagram of a notional power spectral density (PSD)in a “wide band of interest” for cognitive radio, where the horizontalaxis shows frequency and the vertical axis shows the PSD.

FIG. 3 is a plot of Gaussian wavelet, where the vertical axis is theamplitude, and the horizontal can be either time, frequency, distance,etc. depending on the application

FIG. 4 is a flow diagram for the wavelet transformation frequency domainmethod for finding discontinuities in a power spectral density, thediscontinuities corresponding to the boundaries between frequency bandsallocated to licensed users.

FIG. 5 is a flow diagram for the multi-scale product frequency domainmethod for finding discontinuities in a power spectral density, thediscontinuities corresponding to the boundaries between frequency bandsallocated to licensed users.

FIG. 6 is a schematic showing a single threshold energy detector.

FIG. 7 is a schematic of the decision rule for a hard decision made by asingle threshold energy detector.

FIG. 8 is a schematic of the cooperative spectrum sensing (CSS) networkfor cognitive radio using a centralized architecture.

FIG. 9 is a schematic of the cooperative spectrum sensing (CSS) networkfor cognitive radio using a distributed architecture.

FIG. 10 is a schematic of a cooperative spectrum sensing network ofcognitive radio users with a centralized architecture.

FIG. 11 is a flow diagram for the single threshold energy detectiontime-domain method for deciding whether a frequency band allocated tolicensed user is being used the method using data fusion to base thedecision on measurement results from a plurality of N_(U) cognitiveradio users (using the R out of N_(U), also known as K our of L,decision metric).

FIG. 12 is a flow diagram for the equal gain combining time-domainmethod for deciding whether a frequency band allocated to licensed useris being used the method using data fusion to base the decision onmeasurement results from a plurality of N_(U) cognitive radio users.

FIG. 13 is a flow diagram for the hybrid data-decision fusion method fora cooperative spectrum sensing for a network of cognitive radios usersin order to determine if the frequency band in being used.

FIG. 14 is a flow diagram for the improved frequency domain method fordetecting boundaries between frequency bands allocated to PUs, thedetection resulting from finding discontinuities in the power spectraldensity, the method including the improvements of a median filteringstep, a thresholding step, and a multi-scale sum step.

FIG. 15 is a schematic showing a bi-threshold energy detector, where ahard decision of H₁ is made for signals Y_(i) greater than the secondthreshold λ₂, a hard decision of H₀ is made for signals Y_(i) less thanthe second threshold λ₂, and a soft decision is made for signals Y_(i)in the fuzzy region between the first threshold λ₁ and the secondthreshold λ₂.

FIG. 16 is a plot showing the operation of median filter of order 3 asdiscussed in L. Rabiner, M. Sambur, and C. Schmidt, “Applications of anonlinear smoothing algorithm to speech processing,” IEEE Transactionson Acoustics, Speech, and Signal Processing, vol. 23, no. 6, pp.552-557, December 1975.

FIG. 17 is a schematic showing a simple representation of a cognitiveradio cycle as discussed in I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, andS. Mohanty, “NeXt generation/dynamic spectrum access/cognitive radiowireless networks: A survey,” Computer Networks, vol. 50, no. 13, pp.2127-2159, September 2006.

FIG. 18 is branch chart showing the classification of spectrum sensingtechniques.

FIG. 19 is a plot showing a comparison of Fourier transform and Wavelettransform basis functions

FIG. 20 is a diagram showing the first step computation steps forefficient wavelet decomposition as described in S. G. Mallat, “A theoryfor multiresolution signal decomposition: the wavelet representation,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11,no. 7, pp. 674-693, July 1989, herein incorporated by reference in itsentirety, and G. Strang and T. Nguyen, Wavelets and Filter Banks, 2nded. Wellesley College, 1996, p. 520, herein incorporated by reference inits entirety.

FIG. 21 is a branching chart showing a multiple-level waveletdecomposition tree.

FIG. 22 is a plot showing graphically the definitions for probability ofmissed detection and probability of false alarm. The plot also providesa notional example of the decision trade-offs for the choice ofthreshold.

FIG. 23 is a plot showing receiver operating characteristics (ROCs) fordata fusion using OR rule versus decision fusion using equal gaincombining (EGC) under additive white Gaussian noise (SNR=6 dB).

FIG. 24 is a plot showing receiver operating characteristics (ROCs) fordata fusion using OR rule versus decision fusion using equal gaincombining (EGC) under Rayleigh fading (SNR=5 dB).

FIG. 25 is a plot showing simulated results for the (b)multi-scale-product method (i.e. P₁₂₃₄) and (c) multi-scale-sum method(i.e. H₁₂₃₄) of combining wavelet transform coefficients for the purposeof detecting discontinuities in the (a) power spectral density in thepresence of noise. The top plot (a) shows the power spectral density inthe presence of noise. The middle plot (b) shows the result of themulti-scale-product method of combining wavelet transform coefficients.The bottom plot (c) shows the result of the multi-scale-sum method ofcombining wavelet transform coefficients.

FIG. 26 schematic of the cognitive radio processor for performingcalculations and signal processing steps.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views.

The present invention provides an improved method for accurate androbust spectrum sensing to enable efficient usage of spectrum in anenvironment of bandwidth scarcity. Cognitive radio deals withopportunistic bandwidth usage in an environment where licensed primaryusers (PUs) do not always use their allocated bandwidth. The cognitiveradio user (CR) requires robust and accurate spectrum sensing methods todetect spectrum holes that can be used by the CR while a PU is inactive.False positive identification of spectrum holes leads to the CRtransmitting at the same frequency and potentially interfering with aPU, while missed detection of spectrum holes results in lostopportunities for wireless communication. The improved method forspectrum sensing includes a robust frequency-domain method of detectingfrequency bands in the absence of prior knowledge about the frequencybands.

The method of the present invention is an improvement over themulti-scale product method. The method improves the ability of acognitive radio to detect discontinuities in a measured power spectraldensity (PSD), and then determine if the frequency bands bounded bythese discontinuities are being used by a primary user (PU). Thediscontinuities in the PSD correspond to boundaries between frequencyband allocated to PU, the discontinuities arising from practical aspectsof RF communications such as the use of guard bands, choice ofmodulation scheme, differences in received power from different PUs,etc.

In order to overcome the problem of spectrum scarcity and efficientlyutilize of the radio spectrum, the Cognitive Radio approach makes nodes(i.e. individual CRs) aware of their environment, and parameters aremodified in real-time, based on the predicted situation of the targetedfrequency bands. In this way, the foremost operation of a CognitiveRadio is to sense the targeted spectrum, and then make a decision on theavailability of spectrum so that secondary users can benefit from it.Note that the spectrum sensing operation is a very challenging task andneeds to be accurate and efficient in order to enable the CognitiveRadio system to work effectively.

In order to sense the surrounding environment reliably, the spectrumsensing ability of a cognitive radio must be accurate and robust.Spectrum sensing becomes a very challenging task when the cognitive userhas no prior information about the signal characteristics of the primary(licensed) user that might be active in a particular frequency band ofinterest. Besides the inability of the cognitive user to know about theprimary user's signal characteristics beforehand, the situation becomesmore complicated under the so-called fading effect due to environmentalobstacles.

FIG. 1 show the process of spectrum handoff, wherein a cognitive radiouser (CR) transmitting over a licensed frequency band tracks change tothe radio environment, and when a primary user (PU) begins transmittingon the same frequency band as the CR, the CR changes frequency usingalternative unused spectrum. Cognitive radio to improve spectrumutilization benefits to a wide range of frequencies and applicationspaces spanning wireless communication networks including: a cellularsystem (e.g., GSM, CDMA, etc.), a WiFi system, a microwave system, amillimeter-wave radio system, a satellite communication system, etc. Thewide band of interest could contain signals employing many differentmodulation schemes including: analog modulation such as amplitudemodulation, phase modulation, frequency modulation, single side bandmodulation, space modulation, etc. or digital modulation such as phaseshift key modulation, frequency shift key modulation, amplitude shiftkey modulation, quadrature amplitude modulation, quadrature phasemodulation, etc. or any other modulation principle. The PSD will havediscontinuities at the boundaries between frequency bands allocated toPUs as discussed in Z. Tian and G. B. Giannakis, “A Wavelet Approach toWideband Spectrum Sensing for Cognitive Radios,” in 2006 1stInternational Conference on Cognitive Radio Oriented Wireless Networksand Communications, 2006, pp. 1-5.

As with any wireless communication system, the performance degrades inmultipath fading channels. One way to overcome the effects of multipathfading is to use multiple antennas to improve performance. Similarly,fading in wireless channels creates uncertainty in the SNR at the CRreceiver input, making it difficult for the CR to provide a reliabledecision about the absence or presence of the PU, since when the CR isexperiencing a deep fading or shadowing due to large obstacles over theprimary-to-secondary channel, the amount of energy observed during afixed time-bandwidth product, TW, may not be enough to decide about thepresence of a PU. To make the simple energy detection scheme viable, theneighboring secondary users should cooperate. Having neighboring nodesallowed to collaboratively perform the job of spectrum sensing, it wasfound that collaboration can improve sensing performance, mitigate thestringent sensing requirements, and decrease the overall requireddetection time. In addition, the use of cooperation can solve hiddenprimary user problem. The cooperation between multiple CRs can becarried in either a centralized (i.e. FIG. 8) or a distributed fashion(i.e. FIG. 9).

As shown in FIG. 8 a cognitive radio network is formed when multiplecognitive radio users (sometimes called secondary users) cooperate todetermine spectrum holes (sometimes called white spaces) in a RFwireless environment with bandwidth scarcity. The cognitive radio users(CRs)—20, 30, 40, 50, and 60—sense the RF environment through thesensing channel 80 searching for spectrum holes. For our discussion itis assumed that all of the frequency bands within the bandwidth of thecognitive radio users are allocated to licensed primary users (PUs). Forexample, FIG. 8 shows a PU 11. In order to not interfere with thewireless signals of the PUs the CRs can only transmit over an allocatedfrequency band when it is not being used by the PU. Sensing when afrequency band is being used can be difficult for a single CR in anenvironment of channel fading or when the CR is shadowed from the PU'ssignal. More robust detection of spectrum holes can be performed whenCRs cooperate because the channel fading and shadowing varies with theposition of the CR.

When a centralized fusion center (CR0 in FIG. 8) is used to handle thedifferent cognitive decisions, the cooperative spectrum sensing isperformed by: 1) each of the cooperating CRs first senses a targetedfrequency band independently, 2) each cooperating CR reports either theCR's local binary decision or the CR's observation value directly to thefusion center (FC) 70 over the reporting channel, 3) the fusion centerfuses all the received data (or decisions) to infer the presence orabsence of the PU, and transmits the decision result to the CRs.

The FC can be located many places and called by many different namesincluding: common receive, master node, base station, combining node,designated controller. In FIG. 9 a distributed network is shown incontrast to the centralized network shown in FIG. 8. The principle ofoperation is the same for a distributed network except each node (CR)incorporates all the functions of the FC.

As shown in FIG. 8, CR0(FC) 70 is the FC while CR1-CR5, 20, 30, 40, 50,and 60, are the cooperating CRs. When using cooperation among multipleCRs for spectrum sensing, certain protocols need to be defined for thepurpose of sharing sensing information over the reporting channel 19 (incontrast to the reporting channel, the physical point-to-pointconnection between the PU and a CR for the purpose of sensing the PU'ssignal is called a sensing channel 18). Different architecture can beused for the reporting channel 19 such as ISM band and ultra wide band(UWB) as discussed in C. Guo, T. Zhang, Z. Zeng, and C. Feng,“Investigation on Spectrum Sharing Technology Based On Cognitive Radio,”in 2006 First International Conference on Communications and Networkingin China, 2006, pp. 1-5, herein incorporated by reference in itsentirety, and J. Perez-Romero, O. Salient, R. Agusti, and L. Giupponi,“A Novel On-Demand Cognitive Pilot Channel Enabling Dynamic SpectrumAllocation,” in 2007 2nd IEEE International Symposium on New Frontiersin Dynamic Spectrum Access Networks, 2007, pp. 46-54, hereinincorporated by reference in its entirety. Alternatively, the reportingchannel can use a simple protocol using time division multiple access(TDMA) to share the sensing information with the FC, where thecooperating CRs are divided into clusters based on their geographicallocation and send their sensing data to the particular cluster head onlyduring the assigned time slots, as discussed in P. Pawelczak, C. Guo, R.V. Prasad, and R. Hekmat, “Clusterbased spectrum sensing architecturefor opportunistic spectrum access networks,” in IEEE VehicularTechnology Conference VTC2007, 2007, herein incorporated by reference inits entirety.

It is very important to consider that the cooperation mechanism shouldhave as low as possible overhead, and it should be robust to networkchanges and failures. Also, the amount of delay needs to be minimizedfor a particular cooperation algorithm. Usually, such type of protocolsare defined at Medium Access Layer (MAC) as discussed in L. Musavian andT. Le-Ngoc, “Cross-layer design for cognitive radios with joint AMC andARQ under delay QoS constraint,” in 2012 8th International WirelessCommunications and Mobile Computing Conference (IWCMC), 2012, pp.419-424, herein incorporated by reference in its entirety.

When the CRs report a local binary decision to the FC and the FCcombines these local binary decisions to obtain the final decision, theFC process of combining local decisions from the CRs to obtain a finaldecision is called decision fusion (also known as hard combination).When the CRs report observation values, such as the received energyvalue that each CR independently measures when receiving signals fromthe sensing channel, and the FC combines the local observation valuesfrom each CR to obtain a final decision, the process is called datafusion in contrast to decision fusion. The local decision at the CRnetwork nodes are called hard decisions for the decision fusion methodand are called soft decisions when the received energy value is reportedin the data fusion method. Data fusion requires greater reportingchannel bandwidth than for decision fusion which uses only a singlebinary value to report the result for a given frequency band. Although,data fusion imposes large amount of communication overhead over thereporting channel, it has better detection performance than decisionfusion in low signal-to-noise-ratio environment, as discussed in J. Ma,G. Y. Li, and B. H. Juang, “Signal processing in cognitive radio,”Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823, 2009, hereinincorporated by reference in its entirety. By combining decision fusionand data fusion into a hybrid decision-data fusion method at the FC andemploying bi-threshold energy detectors at each CR node in the CRnetwork to measure the sensing channel, the CR network experiences mostof the improved detection benefits of using a data fusion method, butwith the lower overhead of a using decision fusion method.

At the physical layer, the framework of the centralized cooperativespectrum sensing CSS can be represented as shown in FIG. 10. Asdiscussed in I. F. Akyildiz, B. F. Lo, and R. Balakrishnan, “Cooperativespectrum sensing in cognitive radio networks: A survey,” PhysicalCommunication, vol. 4, no. 1, pp. 40-62, March 2011, herein incorporatedby reference in its entirety, the framework consists of the PU 11,cooperating CRs 20, 30, and 40, FC 70, the sensing channel 18, thereporting channel 19, and an optional external database 81, which may belocated remotely.

As shown in the framework, a group of collaborative CRs, presumablyindependent of each other, perform targeted sensing using their RFfrontend 21. The processing unit 22 of a CR may include, among otherthings, a signal processor 23, data fusion 24 and hypothesis testingentities 25. The RF frontend 21 is capable to be configured for datatransmission or local sensing. Besides that, analog-to-digitalconversion will also be done by the RF frontend 21. The localobservations of the cooperating CRs can directly be transmitted to theFC 70, or it can be locally processed at each CR to provide a decisionto the FC 70. Usually, certain amount of processing on the localobservations is needed to minimize the bandwidth requirement over thereporting channels. The processing may include the evaluation of theenergy statistics and thresholds. When the local decision or theobservations are ready, a request to a higher layer (e.g., MAC layer) issent to acquire the access of a control channel. The FC 70 in thecentralized CSS framework can be a powerful cooperating CR which has allthe capabilities as the other CRs. In addition, the FC 70 can have otherfunctionalities, such as user selection 74 and knowledge base 75, toundertake the cooperation tasks successfully. Based on the requirementand the ability of the FC, the FC can be connected to an externaldatabase 81 through an ultra-high speed communication medium 82 (e.g.,fiber optics). This external database 81 will assist the FC and canprovide information regarding the PU 20 activity and spectrum holes.

The proposed method of spectrum sensing to detect spectrum holes usesboth a frequency-domain method and a time-domain method. Thefrequency-domain method finds the boundaries between frequency bandsallocated to PUs by detecting discontinuities in the power spectraldensity PSD. Each CR estimates the PSD at its position by measuring thesensing channel and performing well known processing steps on theresultant measurements. The time-domain method also uses measurements ofthe sensing channel, but considers separately each frequency banddefined by the frequency boundaries found using the frequency-domainmethod. In the time-domain method, for each frequency band the energy ismeasured for a time interval to obtain a received energy value. Thereceived energy value is evaluated and if the CR is part of acooperating network of CRs the evaluation is communicated to a fusioncenter where the final decision is made about whether the frequency bandis being used; or if the CR is acting independently, the CR makes adecision based on the received every value whether the frequency band isused.

In one non-limiting embodiment of the time-domain method, a hybriddata-decision fusion method is used for cooperative spectrum sensing(CSS) in cognitive radio oriented wireless networks (CROWN) in which wecombine hard decisions and soft decisions. A two-threshold energydetector is used at each CR to classify it as either a hard-decision CR(HDCR) or a soft-decision CR (SDCR). While the HDCRs transmit a binarydecision to the fusion center, the SDCRs transmit the received energyvalue.

We consider a centralized CSS network with N CRs. Each of thecooperating CRs uses a bi-threshold energy detector, as shown in FIG.15. The two thresholds λ₁ and λ₂ are used to measure the reliability ofthe decision on the received energy value, Y_(i). The received energyvalue, Y_(i), can fall in one of three regions as shown in FIG. 15. IfY_(i) is less than λ₁ “Decision H₀” is sent, while if Y_(i) exceeds λ₂,“Decision H₁” is sent. The fuzzy region models the situation where theenergy value is not reliable enough for the CR to make a hard decision.The CRs whose received energy falls in the fuzzy region would directlyreport their received energy to the fusion center (FC) 70. Finally, theFC 70 combines all the soft- and hard-decisions into a single finaldecision—deciding whether the frequency band is used or not used.

A flow chart of the hybrid data-decision fusion method is shown in FIG.13. The hybrid data-decision fusion method is performed using thesesteps:

1) Each of the N cooperating CRs performs independent spectrum sensingof the targeted frequency band and, based on the received energy value,Y_(i), sends either its hard-decision (HD_(i)), H₀ or H₁, or thereceived energy value Y_(i) to the fusion center. The fusion center (FC)thus receives the following types of information from each CR:

${FC}_{i} = \{ {\begin{matrix}{Y_{t},} & {\lambda_{1} \leq Y_{i} \leq \lambda_{2}} \\{{HD}_{i},} & {otherwise}\end{matrix},{i = 1},2,\ldots \mspace{14mu},N} $

where, the hard decision HD_(i) can be either H₀ (absent) at which casea binary 0 will be transmitted or H₁ (present) at which case a binary 1will be transmitted.

${HD}_{i} = \{ {\begin{matrix}{0,} & {0 \leq Y_{i} \leq \lambda_{1}} \\{1,} & {Y_{i} \geq \lambda_{2}}\end{matrix}.} $

2) Suppose now that K out of N_(U) cognitive users report HDs, andN_(U)−K users report energies to the fusion center. The fusion centerwill first take an initial decision (soft decision) by adding all thereported raw energies from N_(U)−K users using EGC scheme as discussedin F. F. Digham, M. S. Alouini, and M. K. Simon, “On the energydetection of unknown signals over fading channels,” in IEEEInternational Conference on Communications, 2003. ICC '03, 2003, vol. 5,pp. 3575-3579, herein incorporated in its entirety by reference. Thesoft decision (SD) is represented as follows:

${SD} = \{ {\begin{matrix}{0,} & {0 \leq {\sum\limits_{i = 1}^{N - K}Y_{i}} \leq \lambda} \\{1,} & {{\sum\limits_{i = 1}^{N - K}Y_{i}} \geq \lambda}\end{matrix},} $

where λ used in soft decision can be calculated using Eq. (10) from F.F. Digham, M.-S. Alouini, and M. K. Simon, “On the Energy Detection ofUnknown Signals Over Fading Channels,” IEEE Transactions onCommunications, vol. 55, no. 1, pp. 21-24, January 2007, hereinincorporated in its entirety by reference.3) The fusion center will then make the final decision (FD) as follows:

${FD} = \{ \begin{matrix}{1,} &  {SD} \middle| {{\sum\limits_{i = 1}^{K}{HD}_{i}} \geq 1}  \\{0,} & {otherwise}\end{matrix} $

Hence, the fusion center will assume that the targeted frequency band isavailable for secondary usage only if the combination of hard- andsoft-decision is equal to 0.

Accurate detection of holes in the spectrum (white spaces) is still avery challenging task partially due to the challenge of identifying theboundaries between frequency band in the absence of prior knowledgeabout the frequency bands. The wavelet transform (WT) method is robustand computationally efficient in wideband spectrum sensing. It allowsthe CR to quickly and accurately identify the number of subbands withinthe wide band of interest shown in FIG. 2.

The frequency-domain method for finding edges to frequency bands isdiscussed in Z. Tian and G. B. Giannakis, “A Wavelet Approach toWideband Spectrum Sensing for Cognitive Radios,” in 2006 1stInternational Conference on Cognitive Radio Oriented Wireless Networksand Communications, 2006, pp. 1-5 to avoid spurious wavelet transformcoefficients due to noise. Noise in the estimated PSD sometimes resultsin sharp features in the frequency domain resembling the edge of afrequency band being used by a PU. While using wavelet smoothingfunctions smoothe out much of the sharp spectral features due to noise,more can be done. The frequency-domain method uses median filtering onthe estimated PSD to smooth the PSD before calculating the wavelettransform coefficients. After calculating the wavelet transformcoefficients, a noise threshold is calculated for the wavelet transformcoefficients, and all wavelet transform coefficients below the thresholdare set to zero. Additionally, by taking the multi-scale sum of thewavelet transform coefficients for different scales, uncorrelatedwavelet transform coefficients corresponding to noise are suppressed byaveraging such that it is easier to distinguish between frequency bandboundaries and noise.

FIG. 14 shows a flow chart of the steps in the frequency-domain processincluding: acquiring a time domain signal 311, estimating the PSD 312,median filtering the PSD 331, calculating wavelet transform coefficients313, suppressing wavelet transform coefficients below the noisecoefficient threshold 332, performing a multi-scale sum of the wavelettransform coefficients 333, and solving for PSD discontinuities 314.

There will always be some Gaussian (thermal) noise disturbance at thereceiver. In order to cope with it, we propose to apply Median Filteringto the received signal's PSD S_(r)(ƒ) before calculating the wavelettransform coefficients. Median filter is a nonlinear digital filteringtechnique used to remove noise from a signal while preserving the edgesof the image or signal. Median filtering technique applies slidingwindow to a sequence, where the sliding window runs through the entiresignal entry by entry, replacing the center value in the window with themedian value of all the other points in the window as discussed in M.Gabbouj, E. J. Coyle, and N. C. Gallagher, “An overview of median andstack filtering,” Circuits Systems and Signal Processing, vol. 11, no.1, pp. 7-45, March 1992, herein incorporated by reference in itsentirety. While performing the median filtering operation over a noisysequence, typically, the sliding window is assumed to be of odd length,i.e., having a width of 2N+1, where N is some positive integer. At aparticular instant, suppose the window is centered at sample k in theinput sequence, then the time-ordered window of 2N+1 points can bespecified in the vector form as:

(x _(k−N) ,x _(k−N+1) , . . . ,x _(k) , . . . ,x _(k+N))

The output of the median filter at the time when the window is centeredat sample k in the input sequence, denoted as y_(k), can be representedas:

y _(k)=median(x _(k−N) ,x _(k−N+1) , . . . ,x _(k) , . . . ,x _(k+N))

The samples in the window are first reordered based on their rank(magnitude):

(x ₍₁₎ ,x ₍₂₎ , . . . ,x _((2N+1)))

where x_(i) denoted the sample of the i^(th) rank. For example, if N=2,and the time-ordered samples in the sliding window are:

(x _(k−N) ,x _(k−N+1) , . . . ,x _(k) , . . . ,x _(k+N))=(8,1,6,4,1),

then the rank ordered samples would be:

(x ₍₁₎ ,x ₍₂₎ ,x ₍₃₎ ,x ₍₄₎ ,x ₍₅₎)=(1,1,4,6,8).

Thus the median filter output for this example would simple bey_(k)=x₍₃₎=4. The same procedure would be repeated for all the inputsignal samples.

FIG. 16 shows the operation of a median filter of order 3. As mentionedbefore, one of the key properties of a median filter is that it does notsmear out sharp edges of a square input signal, as long as the durationof the square creating the edge exceeds some critical duration asdiscussed in L. Rabiner, M. Sambur, and C. Schmidt, “Applications of anonlinear smoothing algorithm to speech processing,” IEEE Transactionson Acoustics, Speech, and Signal Processing, vol. 23, no. 6, pp.552-557, December 1975, herein incorporated by reference in itsentirety. This property makes the median filter a good candidate for asignal smoother. This property can be further illustrated using a simpleexample. The input signal x(n) is fed into a 3^(rd) order median filter,where y(n) represents the output of the filter. There exists sharpirregularities in the input signal at n=6 and n=11. As shown, the outputy(n) is found to be exactly the same as input signal. Even afterincreasing the order of median filter to 9, the output y(n) remains thesame. However, increasing the filter order beyond 9 would smoothen outthe discontinuity in x(n) and the output becomes flat. Hence, theselected order of the median filter is dependent on the required minimumduration of discontinuity that should be preserved.

Performing median filtering results in a smooth PSD S_(r)(ƒ), andconsequently less spurious local extrema due to noise have been observedin the wavelet transform curves, however, we did not get rid entirely ofthe unwanted coefficients. Ideally, the order of the median filter ischosen using prior knowledge of the bandwidth of the narrowest bandinside the wideband of interest in order to avoid loss of edgeinformation for the narrowest frequency bands. Without prior knowledge,an iterative search can be performed by varying the filter order andusing feedback on the quality of edges and spurious noise suppression tooptimize the filter order.

The continuous-time wavelet transformation CWT of the PSD is calculatedby convolving the PSD with the wavelet smoothing function

${{\phi_{s}(f)} = {\frac{1}{s}{\phi ( \frac{f}{s} )}}},$

where s is the scale factor. The CWT of the PSD is given by

W _(s) S _(r)(ƒ)=S _(r)*φ_(s)(ƒ).

the result of the convolution in 0 depends mainly upon the values ofS_(r)(ƒ) in association with the specific scale used. Hence,W_(s)S_(r)(ƒ) will provide information on the local structure ofS_(r)(ƒ). It is well understood that irregularities of a function can bewell represented by its derivatives, therefore, the derivative ofS_(r)(ƒ) smoothed by the scaled wavelet φ_(s)(ƒ) will provide therequired information, and is expressed as:

${W_{s}^{\prime}{S_{r}(f)}} = {s\frac{}{f}( {S_{r}*\phi_{s}} ){(f).}}$

So, the local modulus maxima W_(s)′S_(r)(ƒ) (i.e., canny edge detection)represent the edges in the PSD S_(r)(ƒ). More formally, theidentification of frequency boundaries {f_(n)}_(n=1) ^(N−1) can beexpressed as:

{circumflex over (f)} _(n)=maxima_(f) {|W _(s) ′S _(r)(ƒ)|},fε[f ₀ ,f_(N)],

where dyadic scale factors have been used, i.e., s=2^(j), j=1, 2, . . ., J.

Before solving for the maxima of the wavelet transform coefficients(step 314 in FIG. 14), there are several methods for suppressingspurious wavelet transform coefficients due to noise. In FIG. 14 thesemethods are thresholding of noise-coefficients 332, and multi-scale sum333.

The disturbance in the received signal's PSD S_(r)(ƒ) due to thermalnoise is a challenge in estimating the exact boundaries of frequencybands allocated to PUs. The wavelet transform coefficients curvescontain peaks not only due to spectrum edges, but also due noise.Consequently, it is not straightforward to extract frequency edges fromCWT coefficients directly.

As shown in FIG. 14 there is a “thresholding noise-coefficients” step332, to reduce the effects of noise. To suppress, where possible, thewavelet transform coefficient arising from noise, a noise threshold,λ_(Noise), for the wavelet transform coefficient is established. Thisthreshold, λ_(Noise), can be determined based on prior knowledge of theRF front end (i.e. the noise temperature of the receiver, amplifiers,etc.), calibrations or other empirical measurements and data processing.The wavelet transform coefficients are compared to the noise threshold,λ_(Noise), and those coefficients below the noise threshold are set tozero.

As shown in FIG. 14, a “multi-scale sum” step 333, can also be employedbefore or after the “thresholding noise coefficients” step 332 to alsomitigate the effects of noise. The “thresholding noise coefficients”step 332 could also be employed both before and after “multi-scale sum”step 333. Identification of frequency boundaries is improved bycombining wavelet transform coefficients W_(s)′S_(r)(ƒ) of differentscales, with the goal of suppressing the noise-induced spurious localmaxima (which are random at each scale). In combining wavelet transformcoefficients for different dyadic scales, the noise tends to average tozero while the coefficients corresponding to edges remain large.Previously, a multi-scale-product method was proposed as the mechanismfor combining wavelet transform coefficient of different scales.However, the multi-scale-product method works poorly when the frequencybands become very narrow. Because the wavelets perform a smoothingfunction, wavelets with large scale factors tend to smooth together therising and falling edges of a narrow frequency band with the undesiredresult that for large scales the rising and falling edges mostly canceleach other and the wavelet transform coefficients corresponding to theseedges become very small, almost zero. In the multi-scale-product method,the wavelet transform coefficients are multiplicative for each scalefactor. So, when the wavelet transform coefficients for a narrowfrequency band are negligible at even a single scale factor, themulti-scale product for than narrow frequency band will be similarlynegligible. a single the fact small for a single scale factor, thenthose. The multi-scale-product method gives too much weight to absenceof an edge feature in the wavelet transform coefficients with largescales.

On solution to solving this problem is limiting computations to onlysmall scales. However, higher scales have tremendous benefit in the caseof non-ideal PSD in Real Channel Environment as discussed in Y.-L. Xu,H.-S. Zhang, and Z.-H. Han, “The Performance Analysis of SpectrumSensing Algorithms Based on Wavelet Edge Detection,” in 2009 5thInternational Conference on Wireless Communications, Networking andMobile Computing, 2009, pp. 1-4, herein incorporated by reference in itsentirety. At the higher scales, the smooth edges in PSD have highercorrelation with the scaled wavelets and thus are more likely to bedetected with the stretched wavelet.

We propose the multi-scale-sum method as an alternative to themulti-scale-product method. The multi-scale-sum method combinesnegligible for wavelet transform coefficients of different scales bysumming the coefficients, which has the benefit of averaging our andsuppressing coefficients corresponding to noise, but deemphasizes theabsence of a boundary feature at any one scale factor. The multi-scalesum method combines the wavelet transform coefficients of differentscales using the equation

${{H_{J}{S_{r}(f)}} = {\sum\limits_{j = 1}^{J}{W_{s = 2^{j}}^{\prime}{S_{r}(f)}}}},$

And as shown in FIG. 14 as the “multi-scale sum” step 333.

Finally, the discontinuities in the PSD are solved for by finding themaximal values of the multi-scale sum as described by the expression,

{circumflex over (f)} _(n)=maxima_(f) {|H _(J) S _(r)(ƒ)|},fε[f ₀ ,f_(N)],

and as shown in FIG. 14 as the “solve for PSD discontinuities” step 314.

FIG. 25 shows a simulated PSD and the results of combining wavelettransform coefficients using the multi-scale-product method (P₁₂₃₄) andthe multi-scale-sum method (H₁₂₃₄). Whereas, the local maxima of P₁₂₃₄corresponding to B6 are barely perceptible, the local maxima of H₁₂₃₄corresponding to B6 are clearly visible above the noise.

In addition to using the multi-scale sum method to improve detection ofnarrow frequency bands, the method can employ different families ofwavelet smoothing functions such as the Haar and biorthogonal wavelets.These wavelets appear to have better characteristics for edge detectionthan the more commonly used Gaussian wavelets, which were used to obtainthe simulated results in FIG. 25. When the spectrum of interest containsabrupt/sharp changes, as is the case with our simulations, the use ofHaar mother-wavelet is more appropriate to capture the edges at multipleresolutions. On the other hand, Gaussian mother-wavelet was employedwhen the spectrum of interest exhibits smooth edges/singularities. Suchsmooth type of PSD is the result of either the imperfections of the RFfilter in transmitter, or the multipath fading and/or Doppler effect inreal channel environment.

While we have described the spectrum sensing methods in the context ofcognitive radio and wireless communications, these improved spectrumsensing methods could be applied to other fields where it is importantto locate discontinuities in a wide bandwidth signal, and where multipledispersed sensors collaborate to make decision about the presence of asensed phenomenon. For example, the methods could be used in the fieldof acoustics where there is a network of dispersed microphones andspeakers in an environment with channel fading.

Additionally, the suggested improvements to cognitive radio andcognitive radio networks, including using bi-threshold detectors makingboth hard decisions and soft decisions, a hybrid data-decision fusionmethod, median filtering the PSD, suppressing wavelet transformcoefficients below a coefficient noise threshold, and combining wavelettransform coefficients using a multi-scale-sum method can be used alltogether in an improved spectrum sensing method for cognitive radio. Theembodiment incorporating all of these improvements can be summarized byobserving that this embodiment would include both the improvedfrequency-domain method shown in FIG. 5 and the improved time-domainmethod shown in FIG. 14. However, it will also be understood by thoseskilled in the art that an improved spectrum sensing method forcognitive radio can also be realized by incorporating only a subset ofall of the proposed improvements. These methods incorporating varioussubsets of the proposed improvements are alternative embodiments ofimproved spectrum sensing methods.

For example, in a second non-limiting embodiment, the frequency domainmethod shown in FIG. 4 could be used with the improved time-domainmethod shown in FIG. 13. Additionally, a third embodiment of the methodcan be realized by combining the frequency-domain method shown in FIG. 5with the improved time-domain method shown in FIG. 13. In a fourth andfifth embodiment of the spectrum sensing method, the improved frequencydomain method shown in FIG. 14 can be combined with the time-domainmethod shown in FIG. 11, and the improved frequency domain method shownin FIG. 14 14 can be combined with the time-domain method shown in FIG.12. Also, additional permutations of the possible embodiments can berealized by modifying an of the previous embodiments applying theimproved frequency domain method shown in FIG. 14 by modifying theimproved spectrum sensing method to exclude at least one the three stepsin FIG. 14 of median filtering the PSD 331, thresholding ofnoise-coefficients, 332, and multi-scale sum 333.

These improved methods provide a frequency-domain spectrum sensingapproach using the Wavelet transform, and a time-domain spectrum sensingapproach using a double-threshold energy detector and cooperation amongmultiple single-antenna cognitive users.

The main contributions achieved in these methods are: 1) application ofmedian filtering to the received signals' PSD to reduce the effects ofnoise in wavelet-based spectrum sensing, 2) improving the overallwavelet edge detection results by combining wavelet coefficients fromdifferent scales. The detected edges are used to find the spectralholes, 3) comprehensive analysis of different mother wavelets and theirperformance in spectrum sensing, development of a new hybridtwo-threshold energy detector based spectrum sensing algorithm to reducethe cost over the reporting channels under cooperative spectrum sensingscenario.

In summary, the improved method for spectrum sensing using afrequency-domain methods for detecting boundaries between frequencybands and a time-domain method for detecting when frequency bands areoccupied creates significant improvements over previous similar methods.These improvements include, performing median filtering in order tosmooth PSD S_(r)(ƒ), and minimize spurious local extrema due to noise.Furthermore, a simple yet effective method for thresholding thenoise-wavelet-coefficients has been presented. The targeted spectrum wasa wide band spectrum which would require high sampling rates in order toproperly characterize the wide band spectrum. However, we could reducethis complexity by inserting guard bands during CR transmission or whenthe primary goal of the wavelet approach is a rough estimation ofspectrum holes. During off-load hours, there will be spectrum-holes evenwithin a specific band {B_(n)}. In such a case, the overall operation ofthe wavelet approach will not be affected negatively, since the wavelettechnique will still be able to identify those holes.

For the time domain approach, we proposed a hybrid cooperative spectrumsensing algorithm which combines decision fusion and data fusiontechniques using bi-threshold energy detector at the distributed CRs.This hybrid data-decision fusion method, incurs a negligible performanceloss compared the EGC data fusion method, but has the relative advantagethat the average number of reporting bits dramatically decreases fromthat of the EGC data fusion method. Therefore, the proposed algorithmreduces the communication burden over the reporting channels as comparedto EGC.

Processing digitized signals in either the CRs or in the fusion centermay be performed by the apparatus shown in FIG. 28. These processingfunction include, inter alia, the steps of estimating the PSD,calculating the wavelet smoothing function and its derivatives,performing convolutions, taking absolute values, calculating wavelettransforms and wavelet coefficients, performing data fusion and decisionfusion operations, filtering signals, comparing values, demodulating andmodulating signals, down-sampling and up-sampling signal, and variousother digital signal processing tasks.

Next, a hardware description of the CR processor 22 (shown in FIG. 10)performing functions of processing 23, data fusion 24, and hypothesistesting 25 according to exemplary embodiments is described withreference to FIG. 26. Is discussed previously the FC is a powerful CR,and thus the FC may also use a CR processor to perform processingfunctions such as data/decision fusion 72, hypothesis testing 73, userselection 74, etc. In FIG. 26, the CR processor includes a CPU 1200which performs the processes described above. The process data andinstructions may be stored in memory 1202. These processes andinstructions may also be stored on a storage medium disk 1204 such as ahard drive (HDD) or portable storage medium or may be stored remotely.Further, the claimed advancements are not limited by the form of thecomputer-readable media on which the instructions of the inventiveprocess are stored. For example, the instructions may be stored on CDs,DVDs, in FLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard disk or anyother information processing device with which the CR processorcommunicates, such as a server or computer.

Further, the claimed advancements may be provided as a utilityapplication, background daemon, or component of an operating system, orcombination thereof, executing in conjunction with CPU 1200 and anoperating system such as Microsoft Windows 7, UNIX, Solaris, LINUX,Apple MAC-OS and other systems known to those skilled in the art.

CPU 1200 may be a Xenon or Core processor from Intel of America or anOpteron processor from AMD of America, or may be other processor typesthat would be recognized by one of ordinary skill in the art.Alternatively, the CPU 1200 may be implemented on an FPGA, ASIC, PLD orusing discrete logic circuits, as one of ordinary skill in the art wouldrecognize. Further, CPU 1200 may be implemented as multiple processorscooperatively working in parallel to perform the instructions of theinventive processes described above.

The CR processor in FIG. 26 also includes a network controller 1206,such as an Intel Ethernet PRO network interface card from IntelCorporation of America, for interfacing with network of cognitive radiousers. As can be appreciated, the network of cognitive radio users canbe a public network, such as the Internet, or a private network such asan LAN or WAN network, or any combination thereof and can also includePSTN or ISDN sub-networks. The network of cognitive radio users can alsobe wired, such as an Ethernet network, or can be wireless such as acellular network including EDGE, 3G and 4G wireless cellular systems.The wireless network can also be WiFi, Bluetooth, or any other wirelessform of communication that is known.

The CR processor further includes a display controller 1208, such as aNVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA Corporation ofAmerica for interfacing with display 1210, such as a Hewlett PackardHPL2445w LCD monitor. A general purpose I/O interface 1212 interfaceswith a keyboard and/or mouse 1214 as well as a touch screen panel 1216on or separate from display 1210. General purpose I/O interface alsoconnects to a variety of peripherals 1218 including printers andscanners, such as an OfficeJet or DeskJet from Hewlett Packard.

A sound controller 1220 is also provided in the CR processor, such asSound Blaster X-Fi Titanium from Creative, to interface withspeakers/microphone 1222 thereby providing sounds and/or music.

The general purpose storage controller 1224 connects the storage mediumdisk 1204 with communication bus 1226, which may be an ISA, EISA, VESA,PCI, or similar, for interconnecting all of the components of the CRprocessor. A description of the general features and functionality ofthe display 1210, keyboard and/or mouse 1214, as well as the displaycontroller 1208, storage controller 1224, network controller 1206, soundcontroller 1220, and general purpose I/O interface 1212 is omittedherein for brevity as these features are known.

In one embodiment, the method provides a technique to improve thediscriminating boundaries between frequency bands by first calculatingthe wavelet coefficients of the estimated noise, and then using thesecoefficients as threshold to suppress the noise-induced waveletcoefficients of the received signal's power spectral density (PSD).These wavelet coefficients corresponding to noise are used to define awavelet coefficient noise threshold and wavelet coefficients below thisthreshold are suppressed (e.g. they may be set to zero. In this way, theremaining wavelet coefficients of the received signal's PSD will reflectthe actual boundaries of the sub bands inside the targeted wideband ofinterest. Afterwards, we can take average over the detected sub bands tocalculate the average energy with each sub band, hence inferring theoccupancy status of the targeted spectrum.

In one embodiment, the method provides that wavelet coefficients fordifferent scales are linearly combined using a multi-scale sum step inthe method. The multi-scale sum step further improves the detection offrequency edges inside the targeted wideband of interest.

In one embodiment, the method provides that the wavelet transformcoefficients are calculated using first derivatives, or higher orderderivatives of the wavelet smoothing functions, and the magnitude ofthese derivatives of wavelet smoothing functions indicates the size ofthe discontinuity in the PSD. Discontinuities in the PSD signify theboundaries between frequency bands allocated to primary users. Thus,large wavelet transform coefficients signify the boundaries betweenfrequency bands rather than signifying the signals transmitted over thefrequency bands of interest.

The thesis titled “Spectrum Sensing in Time and Frequency Domains”,written and defended by Humayun Khalid Y. Kathuria, for the degree ofMaster of Science in Telecommunication Engineering at King FahdUniversity of Petroleum & Minerals, and dated December 2012, is hereinincorporated by reference in its entirety.

Obviously, numerous modifications and variations of the presentinvention are possible in light of the above teachings. It is thereforeto be understood that within the scope of the appended claims, theinvention may be practiced otherwise than as specifically describedherein.

Thus, the foregoing discussion discloses and describes merely exemplaryembodiments of the present invention. As will be understood by thoseskilled in the art, the present invention may be embodied in otherspecific forms without departing from the spirit or essentialcharacteristics thereof. Accordingly, the disclosure of the presentinvention is intended to be illustrative, but not limiting of the scopeof the invention, as well as other claims. The disclosure, including anyreadily discernible variants of the teachings herein, define, in part,the scope of the foregoing claim terminology such that no inventivesubject matter is dedicated to the public.

1. A method for spectrum sensing for cognitive radio, the methodcomprising: detecting edges of frequency bands, detecting energies infrequency bands, and to deciding whether frequency bands area availableto cognitive radio users; receiving a time-domain signal by a cognitiveradio user; estimating a power spectral density of the time-domainsignal; calculating wavelet transform coefficients at one or more scalefactors by convolving the power spectral density with a first derivativeof a wavelet smoothing function; obtaining a positive signal by takingthe absolute value of all wavelet transform coefficients, and if morethan one wavelet scale factor is used, combining wavelet transformcoefficients of different scales; comparing the positive signal to anoise threshold and where the positive signal is less than the noisethreshold setting the positive signal to zero; detecting one or morefrequency-band edges of the power spectral density by solving for peakfrequencies, wherein the peak frequencies are frequencies of the localmaxima of the positive signal; defining a plurality of frequency bandsas all frequencies between nearest neighbor pairs of frequency-bandedges; determining a received energy value for a first frequency band ofa plurality of frequency bands comparing the received energy value to anenergy threshold; and signaling frequency band availability based on thecomparison between the received energy value and the energy threshold.2. The method according to claim 1, wherein before obtaining a positivesignal the absolute values of the wavelet transform coefficients arecompared to a wavelet coefficient noise threshold and where the absolutevalues of the wavelet transform coefficients are less than the waveletcoefficient noise threshold, the wavelet transform coefficients are setto zero.
 3. The method according to claim 1, wherein before calculatingthe wavelet transform coefficients the power spectral density isfiltered using a median filter.
 4. The method according to claim 3,wherein the step of comparing the received energy value to an energythreshold is performed by a bi-threshold energy detector with a firstenergy threshold and a second energy threshold, wherein the secondenergy threshold is greater than the first energy threshold; where thebi-threshold energy detector signals the frequency band availability andtransmits a signal value; when the received energy value is in the rangebetween the first energy threshold and second energy threshold, thebi-threshold energy detector signals a soft decision and the signalvalue is a continuous number proportional to the received energy value;when the received energy value is greater than the second energythreshold, the bi-threshold detector signals a hard decision and thesignal value is a binary one; and when the received energy value is lessthan the first energy threshold, the bi-threshold detector makes a harddecision and the signal value is a binary zero.
 5. The method accordingto claim 4, wherein the step of signaling frequency band availability isperformed by a fusion center receiving bi-threshold energy detectorsignal values from a cooperative network of a plurality of cognitiveradio users, wherein the steps of making a final decision regardingfrequency band availability include; receiving at a fusion center thebi-threshold energy detector decisions and signal values from thecooperative network of cognitive radio users; processing the softdecisions from the plurality of cognitive radio users to obtain acooperative soft decision regarding frequency band availability;processing the hard decisions from the plurality of cognitive radiousers to obtain a cooperative hard decision regarding frequency bandavailability; making the final decision that the frequency band isavailable if the cooperative hard decision indicates the frequency bandis available and the cooperative soft decision indicates the frequencyband is available, and otherwise making the final decision that thefrequency band is not available; and transmitting the final decision tothe plurality of cognitive radio users in the cooperative network ofcognitive radio users.
 6. The method according to claim 5, wherein thecooperative soft decision is performed by: linear combining the signalvalues for soft decisions from the cooperative network of cognitiveusers and comparing the linear combination of signal values to asoft-decision threshold; making the cooperative soft decision that thefrequency band is not available, if the linear combination of signalvalues is greater than the a soft-decision threshold, otherwise makingthe cooperative soft decision that the frequency band is available; andwherein the cooperative hard decision is performed by: making thecooperative hard decision that the frequency band is available, if allof the signal values for hard decisions from the cooperative network ofcognitive users indicate that the frequency band is available, otherwisemaking the cooperative hard decision that the frequency band is notavailable.
 7. A method for spectrum sensing for cognitive radio, themethod comprising: detecting edges of frequency bands, detectingenergies in frequency bands, and to deciding whether frequency bandsarea available to cognitive radio users; receiving a time-domain signalby a cognitive radio user; estimating a power spectral density of thetime-domain signal; calculating wavelet transform coefficients at one ormore scale factors by convolving the power spectral density with a firstderivative of a wavelet smoothing function; obtaining a positive signalby taking the absolute value of all wavelet transform coefficients, andif more than one wavelet scale factor is used, linear combining wavelettransform coefficients of different scales; detecting one or morefrequency-band edges of the power spectral density by solving for peakfrequencies, wherein the peak frequencies are frequencies of the localmaxima of the positive signal; defining a plurality of frequency bandsas all frequencies between nearest neighbor pairs of frequency-bandedges; determining a received energy value for a first frequency band ofa plurality of frequency bands comparing the received energy value to anenergy threshold; and signaling frequency band availability based on thecomparison between the received energy value and the energy threshold.8. The method according to claim 7, wherein the step of comparing thereceived energy value to an energy threshold is performed by abi-threshold energy detector with a first energy threshold and a secondenergy threshold, wherein the second energy threshold is greater thanthe first energy threshold; where the bi-threshold energy detectorsignals the frequency band availability and transmits a signal value;when the received energy value is in the range between the first energythreshold and second energy threshold, the bi-threshold energy detectorsignals a soft decision and the signal value is a continuous numberproportional to the received energy value; when the received energyvalue is greater than the second energy threshold, the bi-thresholddetector signals a hard decision and the signal value is a binary one;and when the received energy value is less than the first energythreshold, the bi-threshold detector makes a hard decision and thesignal value is a binary zero.
 9. The method according to claim 8,wherein the step of signaling frequency band availability is performedby a fusion center receiving bi-threshold energy detector signal valuesfrom a cooperative network of a plurality of cognitive radio users,wherein the steps of making a final decision regarding frequency bandavailability include; receiving at a fusion center the bi-thresholdenergy detector decisions and signal values from the cooperative networkof cognitive radio users; processing the soft decisions from theplurality of cognitive radio users to obtain a cooperative soft decisionregarding frequency band availability; processing the hard decisionsfrom the plurality of cognitive radio users to obtain a cooperative harddecision regarding frequency band availability; making the finaldecision that the frequency band is available if the cooperative harddecision indicates the frequency band is available and the cooperativesoft decision indicates the frequency band is available, and otherwisemaking the final decision that the frequency band is not available; andtransmitting the final decision to the plurality of cognitive radiousers in the cooperative network of cognitive radio users.
 10. Themethod according to claim 9, wherein the cooperative soft decision isperformed by: linear combining the signal values for soft decisions fromthe cooperative network of cognitive users and comparing the linearcombination of signal values to a soft-decision threshold; making thecooperative soft decision that the frequency band is not available, ifthe linear combination of signal values is greater than the asoft-decision threshold, otherwise making the cooperative soft decisionthat the frequency band is available; and wherein the cooperative harddecision is performed by: making the cooperative hard decision that thefrequency band is available, if all of the signal values for harddecisions from the cooperative network of cognitive users indicate thatthe frequency band is available, otherwise making the cooperative harddecision that the frequency band is not available.
 11. The methodaccording to claim 10, wherein before calculating the wavelet transformcoefficients, the power spectral density is filtered using a medianfilter.
 12. The method according to claim 11, wherein the positivesignal is compared to a noise threshold and where the positive signal isless than the noise threshold setting the positive signal to zero. 13.The method according to claim 12, wherein before obtaining a positivesignal the absolute values of the wavelet transform coefficients arecompared to a wavelet coefficient noise threshold and where the absolutevalues of the wavelet transform coefficients are less than the waveletcoefficient noise threshold, the wavelet transform coefficients are setto zero.
 14. A method for spectrum sensing for cognitive radio, themethod comprising: detecting edges of frequency bands, detectingenergies in frequency bands, and to deciding whether frequency bandsarea available to cognitive radio users; receiving a time-domain signalby a cognitive radio user; estimating a power spectral density of thetime-domain signal; median filtering the power spectral density;calculating wavelet transform coefficients at one or more scale factorsby convolving the power spectral density with a first derivative of awavelet smoothing function; obtaining a positive signal by taking theabsolute value of all wavelet transform coefficients, and if more thanone wavelet scale factor is used, combining wavelet transformcoefficients of different scales; detecting one or more frequency-bandedges of the power spectral density by solving for peak frequencies,wherein the peak frequencies are frequencies of the local maxima of thepositive signal; defining a plurality of frequency bands as allfrequencies between nearest neighbor pairs of frequency-band edges;determining a received energy value for a first frequency band of aplurality of frequency bands comparing the received energy value to anenergy threshold; and signaling frequency band availability based on thecomparison between the received energy value and the energy threshold.15. The method according to claim 14, wherein the step of comparing thereceived energy value to an energy threshold is performed by abi-threshold energy detector with a first energy threshold and a secondenergy threshold, wherein the second energy threshold is greater thanthe first energy threshold; where the bi-threshold energy detectorsignals the frequency band availability and transmits a signal value;when the received energy value is in the range between the first energythreshold and second energy threshold, the bi-threshold energy detectorsignals a soft decision and the signal value is a continuous numberproportional to the received energy value; when the received energyvalue is greater than the second energy threshold, the bi-thresholddetector signals a hard decision and the signal value is a binary one;and when the received energy value is less than the first energythreshold, the bi-threshold detector makes a hard decision and thesignal value is a binary zero.
 16. The method according to claim 15,wherein the step of signaling frequency band availability is performedby a fusion center receiving bi-threshold energy detector signal valuesfrom a cooperative network of a plurality of cognitive radio users,wherein the steps of making a final decision regarding frequency bandavailability include; receiving at a fusion center the bi-thresholdenergy detector decisions and signal values from the cooperative networkof cognitive radio users; processing the soft decisions from theplurality of cognitive radio users to obtain a cooperative soft decisionregarding frequency band availability; processing the hard decisionsfrom the plurality of cognitive radio users to obtain a cooperative harddecision regarding frequency band availability; making the finaldecision that the frequency band is available if the cooperative harddecision indicates the frequency band is available and the cooperativesoft decision indicates the frequency band is available, and otherwisemaking the final decision that the frequency band is not available; andtransmitting the final decision to the plurality of cognitive radiousers in the cooperative network of cognitive radio users.
 17. Themethod according to claim 16, wherein the cooperative soft decision isperformed by: linear combining the signal values for soft decisions fromthe cooperative network of cognitive users and comparing the linearcombination of signal values to a soft-decision threshold; making thecooperative soft decision that the frequency band is not available, ifthe linear combination of signal values is greater than the asoft-decision threshold, otherwise making the cooperative soft decisionthat the frequency band is available; and wherein the cooperative harddecision is performed by: making the cooperative hard decision that thefrequency band is available, if all of the signal values for harddecisions from the cooperative network of cognitive users indicate thatthe frequency band is available, otherwise making the cooperative harddecision that the frequency band is not available.